,,opticks3  ,,or1 ,a  ,,treatise  ,,of  
,,the  ,reflections1 ,refractions1      
,inflections and ,colours  ,,of         
,,light4  ,the ,,fourth ,,edition1      
corrected4  ,by ,sir ,,isaac ,,newton1  
,knt4  ,,london3  ,printed for ,,william
 ,,innys at the ,west-,end of ,st4      
,paul's4 ,,mdccxxx4  ,,title ,,page ,,of
 ,,the #agcj ,,edition     ,,sir ,,isaac
 ,,newton',s ,,advertisements           
,advertisement ,i   ,part of the ensuing
 ,discourse about ,light was written at 
the ,desire of some ,gentlemen of the   
,royal-,society1 in the ,year #afge1 and
 then sent to their ,secretary1 and read
 at their ,meetings1 and the rest was   
added about twelve ,years after to      
complete the ,theory2 except the third  
,book1 and the last ,proposition of the 
,second1 which were since put together  
out of scatter'd ,papers4 ,to avoid     
being engaged in ,disputes about these  
,matters1 ,i have hitherto delayed the  
printing1 and should still have delayed 
it1 had not the ,importunity of ,friends

 prevailed upon me4 ,if any other       
,papers writ on this ,subject are got   
out of my ,hands they are imperfect1 and
 were perhaps written before ,i had     
tried all the ,experiments here set     
down1 and fully satisfied my self about 
the ,laws of ,refractions and           
,composition of ,colours4 ,i have here  
publish'd what ,i think proper to come  
abroad1 wishing that it may not be      
translated into another ,language       
without my ,consent4  ,the ,crowns of   
,colours1 which sometimes appear about  
the ,sun and ,moon1 ,i have endeavoured 
to give an ,account of2 but for want of 
sufficient ,observations leave that     
,matter to be farther examined4 ,the    
,subject of the ,third ,book ,i have    
also left imperfect1 not having tried   
all the ,experiments which ,i intended  
when ,i was about these ,matters1 nor   
repeated some of those which ,i did try1
 until ,i had satisfied my self about   
all their ,circumstances4 ,to           
communicate what ,i have tried1 and     

leave the rest to others for farther    
,enquiry1 is all my ,design in          
publishing these ,papers4  ,in a ,letter
 written to ,mr4 ,leibnitz in the year  
#afgi1 and published by ,dr4 ,wallis1 ,i
 mention'd a ,method by which ,i had    
found some general ,theorems about      
squaring ,curvilinear ,figures1 or      
comparing them with the ,conic          
,sections1 or other the simplest        
,figures with which they may be         
compared4 ,and some ,years ago ,i lent  
out a ,manuscript containing such       
,theorems1 and having since met with    
some ,things copied out of it1 ,i have  
on this ,occasion made it publick1      
prefixing to it an ,introduction1 and   
subjoining a ,scholium concerning that  
,method4 ,and ,i have joined with it    
another small ,tract concerning the     
,curvilinear ,figures of the ,second    
,kind1 which was also written many      
,years ago1 and made known to some      
,friends1 who have solicited the making 
it publick4                             

,i4 ,n4  ,april #a1 #agjd4              
,advertisement ,,ii  ,in this ,second   
,edition of these ,opticks ,i have      
omitted the ,mathematical ,tracts       
publish'd at the ,end of the former     
,edition1 as not belonging to the       
,subject4 ,and at the ,end of the ,third
 ,book ,i have added some ,questions4   
,and to shew that ,i do not take        
,gravity for an essential ,property of  
,bodies1 ,i have added one ,question    
concerning its ,cause1 chusing to       
propose it by way of a ,question1       
because ,i am not yet satisfied about it
 for want of ,experiments4              
,i4 ,n4  ,july #af1 #agag4              
,advertisement to this ,fourth ,edition 
,this new ,edition of ,sir ,isaac       
,newton's ,opticks is carefully printed 
from the ,third ,edition1 as it was     
corrected by the ,author's own ,hand1   
and left before his ,death with the     
,bookseller4 ,since ,sir ,isaac's       
,lectiones ,opticae1 which he publickly 
read in the ,university of ,cambridge in

 the ,years #affi1 #afgj1 and #afga1 are
 lately printed1 it has been thought    
proper to make at the bottom of the     
,pages several ,citations from thence1  
where may be found the ,demonstrations1 
which the ,author omitted in these      
,opticks4         99       99       99  
99       99  ,transcriber's ,note3      
,there are several greek letters used in
 the descriptions of the illustrations4 
,they are signified by ,greek3 letter4  
,square roots are noted by the letters  
sqrt before the equation4         99    
99       99       99       99  ,,the    
,,first ,,book ,,of ,,opticks     ,,part
 ,i4   ,my ,design in this ,book is not 
to explain the ,properties of ,light by 
,hypotheses1 but to propose and prove   
them by ,reason and ,experiments3 ,in   
order to which ,i shall premise the     
following ,definitions and ,axioms4     
,,definitions   ,,defin4 ,i4  ,by the   
,rays of ,light ,i understand its least 
,parts1 and those as well ,successive in
 the same ,lines1 as ,contemporary in   

several ,lines4 ,for it is manifest that
 ,light consists of ,parts1 both        
,successive and ,contemporary2 because  
in the same place you may stop that     
which comes one moment1 and let pass    
that which comes presently after2 and in
 the same time you may stop it in any   
one place1 and let it pass in any other4
 ,for that part of ,light which is      
stopp'd cannot be the same with that    
which is let pass4 ,the least ,light or 
part of ,light1 which may be stopp'd    
alone without the rest of the ,light1 or
 propagated alone1 or do or suffer any  
thing alone1 which the rest of the      
,light doth not or suffers not1 ,i call 
a ,ray of ,light4   ,,defin4 ,,ii4      
,refrangibility of the ,rays of ,light1 
is their ,disposition to be refracted or
 turned out of their ,way in passing out
 of one transparent ,body or ,medium    
into another4 ,and a greater or less    
,refrangibility of ,rays1 is their      
,disposition to be turned more or less  
out of their ,way in like ,incidences on

 the same ,medium4 ,mathematicians      
usually consider the ,rays of ,light to 
be ,lines reaching from the luminous    
,body to the ,body illuminated1 and the 
refraction of those ,rays to be the     
bending or breaking of those lines in   
their passing out of one ,medium into   
another4 ,and thus may ,rays and        
,refractions be considered1 if ,light be
 propagated in an instant4 ,but by an   
,argument taken from the ,a,equations of
 the times of the ,eclipses of          
,jupiter's ,satellites1 it seems that   
,light is propagated in time1 spending  
in its passage from the ,sun to us about
 seven ,minutes of time3 ,and therefore 
,i have chosen to define ,rays and      
,refractions in such general terms as   
may agree to ,light in both cases4      
,,defin4 ,,iii4  ,reflexibility of      
,rays1 is their ,disposition to be      
reflected or turned back into the same  
,medium from any other ,medium upon     
whose ,surface they fall4 ,and ,rays are
 more or less reflexible1 which are     

turned back more or less easily4 ,as if 
,light pass out of a ,glass into ,air1  
and by being inclined more and more to  
the common ,surface of the ,glass and   
,air1 begins at length to be totally    
reflected by that ,surface2 those sorts 
of ,rays which at like ,incidences are  
reflected most copiously1 or by         
inclining the ,rays begin soonest to be 
totally reflected1 are most reflexible4 
,,defin4 ,,iv4  ,the ,angle of          
,incidence is that ,angle1 which the    
,line described by the incident ,ray    
contains with the ,perpendicular to the 
reflecting or refracting ,surface at the
 ,point of ,incidence4   ,,defin4 ,v4   
,the ,angle of ,reflexion or            
,refraction1 is the ,angle which the    
line described by the reflected or      
refracted ,ray containeth with the      
,perpendicular to the reflecting or     
refracting ,surface at the ,point of    
,incidence4   ,,defin4 ,,vi4  ,the      
,sines of ,incidence1 ,reflexion1 and   
,refraction1 are the ,sines of the      

,angles of ,incidence1 ,reflexion1 and  
,refraction4   ,,defin4 ,,vii  ,the     
,light whose ,rays are all alike        
,refrangible1 ,i call ,simple1          
,homogeneal and ,similar2 and that whose
 ,rays are some more ,refrangible than  
others1 ,i call ,compound1 ,heterogeneal
 and ,dissimilar4 ,the former ,light ,i 
call ,homogeneal1 not because ,i would  
affirm it so in all respects1 but       
because the ,rays which agree in        
,refrangibility1 agree at least in all  
those their other ,properties which ,i  
consider in the following ,discourse4   
,,defin4 ,,viii4  ,the ,colours of      
,homogeneal ,lights1 ,i call ,primary1  
,homogeneal and ,simple2 and those of   
,heterogeneal ,lights1 ,heterogeneal and
 ,compound4 ,for these are always       
compounded of the colours of ,homogeneal
 ,lights2 as will appear in the         
following ,discourse4     ,,axioms4     
,,ax4 ,i4  ,the ,angles of ,reflexion   
and ,refraction1 lie in one and the same
 ,plane with the ,angle of ,incidence4  

,,ax4 ,,ii4  ,the ,angle of ,reflexion  
is equal to the ,angle of ,incidence4   
,,ax4 ,,iii4  ,if the refracted ,ray be 
returned directly back to the ,point of 
,incidence1 it shall be refracted into  
the ,line before described by the       
incident ,ray4   ,,ax4 ,,iv4            
,refraction out of the rarer ,medium    
into the denser1 is made towards the    
,perpendicular2 that is1 so that the    
,angle of ,refraction be less than the  
,angle of ,incidence4   ,,ax4 ,v4  ,the 
,sine of ,incidence is either accurately
 or very nearly in a given ,ratio to the
 ,sine of ,refraction4  ,whence if that 
,proportion be known in any one         
,inclination of the incident ,ray1 'tis 
known in all the ,inclinations1 and     
thereby the ,refraction in all cases of 
,incidence on the same refracting ,body 
may be determined4 ,thus if the         
,refraction be made out of ,air into    
,water1 the ,sine of ,incidence of the  
red ,light is to the ,sine of its       
,refraction as #d to #c4 ,if out of ,air

 into ,glass1 the ,sines are as #ag to  
#aa4 ,in ,light of other ,colours the   
,sines have other ,proportions3 but the 
difference is so little that it need    
seldom be considered4  ,illustration3   
,,fig4 #a  ,suppose therefore1 that ,,rs
 in ,fig4 #a4 represents the ,surface of
 stagnating ,water1 and that ,c is the  
point of ,incidence in which any ,ray   
coming in the ,air from ,a in the ,line 
,,ac is reflected or refracted1 and ,i  
would know whither this ,ray shall go   
after ,reflexion or ,refraction3 ,i     
erect upon the ,surface of the ,water   
from the point of ,incidence the        
,perpendicular ,,cp and produce it      
downwards to ,q1 and conclude by the    
first ,axiom1 that the ,ray after       
,reflexion and ,refraction1 shall be    
found somewhere in the ,plane of the    
,angle of ,incidence ,,acp produced4 ,i 
let fall therefore upon the             
,perpendicular ,,cp the ,sine of        
,incidence ,,ad2 and if the reflected   
,ray be desired1 ,i produce ,,ad to ,b  

so that ,,db be equal to ,,ad1 and draw 
,,cb4 ,for this ,line ,,cb shall be the 
reflected ,ray2 the ,angle of ,reflexion
 ,,bcp and its ,sine ,,bd being equal to
 the ,angle and ,sine of ,incidence1 as 
they ought to be by the second ,axiom1  
,but if the refracted ,ray be desired1  
,i produce ,,ad to ,h1 so that ,,dh may 
be to ,,ad as the ,sine of ,refraction  
to the ,sine of ,incidence1 that is1 7if
 the ,light be red7 as #c to #d2 and    
about the ,center ,c and in the ,plane  
,,acp with the ,radius ,,ca describing a
 ,circle ,,abe1 ,i draw a parallel to   
the ,perpendicular ,,cpq1 the ,line ,,he
 cutting the ,circumference in ,e1 and  
joining ,,ce1 this ,line ,,ce shall be  
the ,line of the refracted ,ray4 ,for if
 ,,ef be let fall perpendicularly on the
 ,line ,,pq1 this ,line ,,ef shall be   
the ,sine of ,refraction of the ,ray    
,,ce1 the ,angle of ,refraction being   
,,ecq2 and this ,sine ,,ef is equal to  
,,dh1 and consequently in ,proportion to
 the ,sine of ,incidence ,,ad as #c to  

#d4  ,in like manner1 if there be a     
,prism of ,glass 7that is1 a ,glass     
bounded with two ,equal and ,parallel   
,triangular ends1 and three plain and   
well polished ,sides1 which meet in     
three ,parallel ,lines running from the 
three ,angles of one end to the three   
,angles of the other end7 and if the    
,refraction of the ,light in passing    
cross this ,prism be desired3 ,let ,,acb
 in ,fig4 #b4 represent a ,plane cutting
 this ,prism transversly to its three   
,parallel lines or edges there where the
 ,light passeth through it1 and let ,,de
 be the ,ray incident upon the first    
side of the ,prism ,,ac where the ,light
 goes into the ,glass2 and by putting   
the ,proportion of the ,sine of         
,incidence to the ,sine of ,refraction  
as #ag to #aa find ,,ef the first       
refracted ,ray4 ,then taking this ,ray  
for the ,incident ,ray upon the second  
side of the ,glass ,,bc where the ,light
 goes out1 find the next refracted ,ray 
,,fg by putting the ,proportion of the  

,sine of ,incidence to the ,sine of     
,refraction as #aa to #ag4 ,for if the  
,sine of ,incidence out of ,air into    
,glass be to the ,sine of ,refraction as
 #ag to #aa1 the ,sine of ,incidence out
 of ,glass into ,air must on the        
contrary be to the ,sine of ,refraction 
as #aa to #ag1 by the third ,axiom4     
,illustration3 ,,fig4 #b4  ,much after  
the same manner1 if ,,acbd in ,fig4 #c4 
represent a ,glass spherically convex on
 both sides 7usually called a ,lens1    
such as is a ,burning-glass1 or         
,spectacle-glass1 or an ,object-glass of
 a ,telescope7 and it be required to    
know how ,light falling upon it from any
 lucid point ,q shall be refracted1 let 
,,qm represent a ,ray falling upon any  
point ,m of its first spherical ,surface
 ,,acb1 and by erecting a ,perpendicular
 to the ,glass at the point ,m1 find the
 first refracted ,ray ,,mn by the       
,proportion of the ,sines #ag to #aa4   
,let that ,ray in going out of the      
,glass be incident upon ,n1 and then    

find the second refracted ,ray ,nq by   
the ,proportion of the ,sines #aa to    
#ag4 ,and after the same manner may the 
,refraction be found when the ,lens is  
convex on one side and plane or concave 
on the other1 or concave on both sides4 
,illustration3 ,,fig4 #c4   ,,ax4 ,,vi4 
,homogeneal ,rays which flow from       
several ,points of any ,object1 and fall
 perpendicularly or almost              
perpendicularly on any reflecting or    
refracting ,plane or spherical ,surface1
 shall afterwards diverge from so many  
other ,points1 or be parallel to so many
 other ,lines1 or converge to so many   
other ,points1 either accurately or     
without any sensible ,error4 ,and the   
same thing will happen1 if the ,rays be 
reflected or refracted successively by  
two or three or more ,plane or          
,spherical ,surfaces4  ,the ,point from 
which ,rays diverge or to which they    
converge may be called their ,focus4    
,and the ,focus of the incident ,rays   
being given1 that of the reflected or   

refracted ones may be found by finding  
the ,refraction of any two ,rays1 as    
above2 or more readily thus4  ,cas4 #a4 
,let ,,acb in ,fig4 #d4 be a reflecting 
or refracting ,plane1 and ,q the ,focus 
of the incident ,rays1 and ,qq,c a      
,perpendicular to that ,plane4 ,and if  
this ,perpendicular be produced to q1 so
 that q,c be equal to ,,qc1 the ,point q
 shall be the ,focus of the reflected   
,rays3 ,or if q,c be taken on the same  
side of the ,plane with ,,qc1 and in    
proportion to ,,qc as the ,sine of      
,incidence to the ,sine of ,refraction1 
the ,point q shall be the ,focus of the 
refracted ,rays4  ,illustration3 ,,fig4 
#d4  ,cas4 #b4 ,let ,,acb in ,fig4 #e4  
be the reflecting ,surface of any       
,sphere whose ,centre is ,e4 ,bisect any
 ,radius thereof1 7suppose ,,ec7 in ,t1 
and if in that ,radius on the same side 
the ,point ,t you take the ,points ,q   
and q1 so that ,,tq1 ,,te1 and ,tq1 be  
continual ,proportionals1 and the ,point
 ,q be the ,focus of the incident ,rays1

 the ,point q shall be the ,focus of the
 reflected ones4  ,illustration3 ,,fig4 
#e4  ,cas4 #c4 ,let ,,acb in ,fig4 #f4  
be the refracting ,surface of any       
,sphere whose ,centre is ,e4 ,in any    
,radius thereof ,,ec produced both ways 
take ,,et and ,ct equal to one another  
and severally in such ,proportion to    
that ,radius as the lesser of the ,sines
 of ,incidence and ,refraction hath to  
the difference of those ,sines4 ,and    
then if in the same ,line you find any  
two ,points ,q and q1 so that ,,tq be to
 ,,et as ,et to tq1 taking tq the       
contrary way from t which ,,tq lieth    
from ,t1 and if the ,point ,q be the    
,focus of any incident ,rays1 the ,point
 q shall be the ,focus of the refracted 
ones4  ,illustration3 ,,fig4 #f4  ,and  
by the same means the ,focus of the     
,rays after two or more ,reflexions or  
,refractions may be found4              
,illustration3 ,,fig4 #g4  ,cas4 #d4    
,let ,,acbd in ,fig4 #g4 be any         
refracting ,lens1 spherically ,convex or

 ,concave or ,plane on either side1 and 
let ,,cd be its ,axis 7that is1 the     
,line which cuts both its ,surfaces     
perpendicularly1 and passes through the 
,centres of the ,spheres17 and in this  
,axis produced let ,f and f be the ,foci
 of the refracted ,rays found as above1 
when the incident ,rays on both sides   
the ,lens are parallel to the same      
,axis2 and upon the ,diameter ,ff       
bisected in ,e1 describe a ,circle4     
,suppose now that any ,point ,q be the  
,focus of any incident ,rays4 ,draw ,,qe
 cutting the said ,circle in ,t and t1  
and therein take tq in such proportion  
to t,e as t,e or ,,te hath to ,,tq4 ,let
 tq lie the contrary way from t which   
,,tq doth from ,t1 and q shall be the   
,focus of the refracted ,rays without   
any sensible ,error1 provided the ,point
 ,q be not so remote from the ,axis1 nor
 the ,lens so broad as to make any of   
the ,rays fall too obliquely on the     
refracting ,surfaces4,a  ,and by the    
like ,operations may the reflecting or  

refracting ,surfaces be found when the  
two ,foci are given1 and thereby a ,lens
 be formed1 which shall make the ,rays  
flow towards or from what ,place you    
please4,b  ,so then the ,meaning of this
 ,axiom is1 that if ,rays fall upon any 
,plane or ,spherical ,surface or ,lens1 
and before their ,incidence flow from or
 towards any ,point ,q1 they shall after
 ,reflexion or ,refraction flow from or 
towards the ,point q found by the       
foregoing ,rules4 ,and if the incident  
,rays flow from or towards several      
points ,q1 the reflected or refracted   
,rays shall flow from or towards so many
 other ,points q found by the same      
,rules4 ,whether the reflected and      
refracted ,rays flow from or towards the
 ,point q is easily known by the        
situation of that ,point4 ,for if that  
,point be on the same side of the       
reflecting or refracting ,surface or    
,lens with the ,point ,q1 and the       
incident ,rays flow from the ,point ,q1 
the reflected flow towards the ,point q 

and the refracted from it2 and if the   
incident ,rays flow towards ,q1 the     
reflected flow from q1 and the refracted
 towards it4 ,and the contrary happens  
when q is on the other side of the      
,surface4   ,,ax4 ,,vii4  ,wherever the 
,rays which come from all the ,points of
 any ,object meet again in so many      
,points after they have been made to    
converge by ,reflection or ,refraction1 
there they will make a ,picture of the  
,object upon any white ,body on which   
they fall4  ,so if ,,pr in ,fig4 #c4    
represent any ,object without ,doors1   
and ,,ab be a ,lens placed at a hole in 
the ,window-shut of a dark ,chamber1    
whereby the ,rays that come from any    
,point ,q of that ,object are made to   
converge and meet again in the ,point q2
 and if a ,sheet of white ,paper be held
 at q for the ,light there to fall upon 
it1 the ,picture of that ,object ,,pr   
will appear upon the ,paper in its      
proper shape and ,colours4 ,for as the  
,light which comes from the ,point ,q   

goes to the ,point q1 so the ,light     
which comes from other ,points ,p and ,r
 of the ,object1 will go to so many     
other correspondent ,points p and r 7as 
is manifest by the sixth ,axiom27 so    
that every ,point of the ,object shall  
illuminate a correspondent ,point of the
 ,picture1 and thereby make a ,picture  
like the ,object in ,shape and ,colour1 
this only excepted1 that the ,picture   
shall be inverted4 ,and this is the     
,reason of that vulgar ,experiment of   
casting the ,species of ,objects from   
abroad upon a ,wall or ,sheet of white  
,paper in a dark ,room4  ,in like       
manner1 when a ,man views any ,object   
,,pqr1 in ,fig4 #h4 the ,light which    
comes from the several ,points of the   
,object is so refracted by the          
transparent skins and humours of the    
,eye1 7that is1 by the outward coat     
,,efg1 called the ,tunica ,cornea1 and  
by the crystalline humour ,,ab which is 
beyond the ,pupil mk7 as to converge and
 meet again in so many ,points in the   

bottom of the ,eye1 and there to paint  
the ,picture of the ,object upon that   
skin 7called the ,tunica ,retina7 with  
which the bottom of the ,eye is covered4
 ,for ,anatomists1 when they have taken 
off from the bottom of the ,eye that    
outward and most thick ,coat called the 
,dura ,mater1 can then see through the  
thinner ,coats1 the ,pictures of        
,objects lively painted thereon4 ,and   
these ,pictures1 propagated by ,motion  
along the ,fibres of the ,optick ,nerves
 into the ,brain1 are the cause of      
,vision4 ,for accordingly as these      
,pictures are perfect or imperfect1 the 
,object is seen perfectly or            
imperfectly4 ,if the ,eye be tinged with
 any colour 7as in the ,disease of the  
,jaundice7 so as to tinge the ,pictures 
in the bottom of the ,eye with that     
,colour1 then all ,objects appear tinged
 with the same ,colour4 ,if the ,humours
 of the ,eye by old ,age decay1 so as by
 shrinking to make the ,cornea and ,coat
 of the ,crystalline ,humour grow       

flatter than before1 the ,light will not
 be refracted enough1 and for want of a 
sufficient ,refraction will not converge
 to the bottom of the ,eye but to some  
place beyond it1 and by consequence     
paint in the bottom of the ,eye a       
confused ,picture1 and according to the 
,indistinctness of this ,picture the    
,object will appear confused4 ,this is  
the reason of the decay of sight in old 
,men1 and shews why their ,sight is     
mended by ,spectacles4 ,for those       
,convex glasses supply the defect of    
plumpness in the ,eye1 and by increasing
 the ,refraction make the ,rays converge
 sooner1 so as to convene distinctly at 
the bottom of the ,eye if the ,glass    
have a due degree of convexity4 ,and the
 contrary happens in short-sighted ,men 
whose ,eyes are too plump4 ,for the     
,refraction being now too great1 the    
,rays converge and convene in the ,eyes 
before they come at the bottom2 and     
therefore the ,picture made in the      
bottom and the ,vision caused thereby   

will not be distinct1 unless the ,object
 be brought so near the ,eye as that the
 place where the converging ,rays       
convene may be removed to the bottom1 or
 that the plumpness of the ,eye be taken
 off and the ,refractions diminished by 
a ,concave-glass of a due degree of     
,concavity1 or lastly that by ,age the  
,eye grow flatter till it come to a due 
,figure3 ,for short-sighted ,men see    
remote ,objects best in ,old ,age1 and  
therefore they are accounted to have the
 most lasting ,eyes4  ,illustration3    
,,fig4 #h4   ,,ax4 ,,viii4  ,an ,object 
seen by ,reflexion or ,refraction1      
appears in that place from whence the   
,rays after their last ,reflexion or    
,refraction diverge in falling on the   
,spectator's ,eye4  ,illustration3      
,,fig4 #i4  ,if the ,object ,a in ,,fig4
 #i4 be seen by ,reflexion of a         
,looking-glass mn1 it shall appear1 not 
in its proper place ,a1 but behind the  
,glass at a1 from whence any ,rays ,,ab1
 ,,ac1 ,,ad1 which flow from one and the

 same ,point of the ,object1 do after   
their ,reflexion made in the ,points ,b1
 ,c1 ,d1 diverge in going from the      
,glass to ,e1 ,f1 ,g1 where they are    
incident on the ,spectator's ,eyes4 ,for
 these ,rays do make the same ,picture  
in the bottom of the ,eyes as if they   
had come from the ,object really placed 
at a without the ,interposition of the  
,looking-glass2 and all ,vision is made 
according to the place and shape of that
 ,picture4  ,in like manner the ,object 
,d in ,,fig4 #b4 seen through a ,prism1 
appears not in its proper place ,d1 but 
is thence translated to some other place
 d situated in the last refracted ,ray  
,,fg drawn backward from ,f to d4       
,illustration3 ,,fig4 #aj4  ,and so the 
,object ,q in ,,fig4 #aj4 seen through  
the ,lens ,,ab1 appears at the place q  
from whence the ,rays diverge in passing
 from the ,lens to the ,eye4 ,now it is 
to be noted1 that the ,image of the     
,object at q is so much bigger or lesser
 than the ,object it self at ,q1 as the 

distance of the ,image at q from the    
,lens ,,ab is bigger or less than the   
distance of the ,object at ,q from the  
same ,lens4 ,and if the ,object be seen 
through two or more such ,convex or     
,concave-glasses1 every ,glass shall    
make a new ,image1 and the ,object shall
 appear in the place of the bigness of  
the last ,image4 ,which consideration   
unfolds the ,theory of ,microscopes and 
,telescopes4 ,for that ,theory consists 
in almost nothing else than the         
describing such ,glasses as shall make  
the last ,image of any ,object as       
distinct and large and luminous as it   
can conveniently be made4  ,i have now  
given in ,axioms and their ,explications
 the sum of what hath hitherto been     
treated of in ,opticks4 ,for what hath  
been generally agreed on ,i content my  
self to assume under the notion of      
,principles1 in order to what ,i have   
farther to write4 ,and this may suffice 
for an ,introduction to ,readers of     
quick ,wit and good ,understanding not  

yet versed in ,opticks3 ,although those 
who are already acquainted with this    
,science1 and have handled ,glasses1    
will more readily apprehend what        
followeth4  ,,footnotes3  ,a ,in our    
,author's ,lectiones ,opticae1 ,part ,i4
 ,sect4 ,,iv4 ,prop #bi1 #cj1 there is  
an elegant ,method of determining these 
,foci2 not only in spherical ,surfaces1 
but likewise in any other curved ,figure
 whatever3 ,and in ,prop4 #cb1 #cc1 the 
same thing is done for any ,ray lying   
out of the ,axis4  ,b ,ibid4 ,prop4 #cd4
     ,,propositions4    ,,prop4 ,i4     
,,theor4 ,i4  ,lights which differ in   
,colour1 differ also in ,degrees of     
,refrangibility4  ,the ,,proof by       
,experiments4  ,exper4 #a4  ,i took a   
black oblong stiff ,paper terminated by 
,parallel ,sides1 and with a            
,perpendicular right ,line drawn cross  
from one ,side to the other1            
distinguished it into two equal ,parts4 
,one of these parts ,i painted with a   
red colour and the other with a blue4   

,the ,paper was very black1 and the     
,colours intense and thickly laid on1   
that the ,phaenomenon might be more     
conspicuous4 ,this ,paper ,i view'd     
through a ,prism of solid ,glass1 whose 
two ,sides through which the ,light     
passed to the ,eye were plane and well  
polished1 and contained an ,angle of    
about sixty degrees2 which ,angle ,i    
call the refracting ,angle of the       
,prism4 ,and whilst ,i view'd it1 ,i    
held it and the ,prism before a ,window 
in such manner that the ,sides of the   
,paper were parallel to the ,prism1 and 
both those ,sides and the ,prism were   
parallel to the ,horizon1 and the cross 
,line was also parallel to it3 and that 
the ,light which fell from the ,window  
upon the ,paper made an ,angle with the 
,paper1 equal to that ,angle which was  
made with the same ,paper by the ,light 
reflected from it to the ,eye4 ,beyond  
the ,prism was the ,wall of the ,chamber
 under the ,window covered over with    
black ,cloth1 and the ,cloth was        

involved in ,darkness that no ,light    
might be reflected from thence1 which in
 passing by the ,edges of the ,paper to 
the ,eye1 might mingle itself with the  
,light of the ,paper1 and obscure the   
,phaenomenon thereof4 ,these things     
being thus ordered1 ,i found that if the
 refracting ,angle of the ,prism be     
turned upwards1 so that the ,paper may  
seem to be lifted upwards by the        
,refraction1 its blue half will be      
lifted higher by the ,refraction than   
its red half4 ,but if the refracting    
,angle of the ,prism be turned downward1
 so that the ,paper may seem to be      
carried lower by the ,refraction1 its   
blue half will be carried something     
lower thereby than its red half4        
,wherefore in both ,cases the ,light    
which comes from the blue half of the   
,paper through the ,prism to the ,eye1  
does in like ,circumstances suffer a    
greater ,refraction than the ,light     
which comes from the red half1 and by   
consequence is more refrangible4        

,illustration4 ,in the eleventh ,figure1
 ,,mn represents the ,window1 and ,,de  
the ,paper terminated with parallel     
,sides ,,dj and ,,he1 and by the        
transverse ,line ,,fg distinguished into
 two halfs1 the one ,,dg of an intensely
 blue ,colour1 the other ,,fe of an     
intensely red4 ,and ,,baccab represents 
the ,prism whose refracting ,planes     
,,abba and ,,acca meet in the ,edge of  
the refracting ,angle ,aa4 ,this ,edge  
,aa being upward1 is parallel both to   
the ,horizon1 and to the                
,parallel-,edges of the ,paper ,,dj and 
,,he1 and the transverse ,line ,,fg is  
perpendicular to the ,plane of the      
,window4 ,and de represents the ,image  
of the ,paper seen by ,refraction       
upwards in such manner1 that the blue   
half ,,dg is carried higher to dg than  
the red half ,,fe is to fe1 and         
therefore suffers a greater ,refraction4
 ,if the ,edge of the refracting ,angle 
be turned downward1 the ,image of the   
,paper will be refracted downward2      

suppose to ,greek3 de1 and the blue half
 will be refracted lower to ,greek3 dg  
than the red half is to ,greek3 pe4     
,illustration3 ,,fig4 #aa4  ,exper4 #b4 
,about the aforesaid ,paper1 whose two  
halfs were painted over with red and    
blue1 and which was stiff like thin     
,pasteboard1 ,i lapped several times a  
slender ,thred of very black ,silk1 in  
such manner that the several parts of   
the ,thred might appear upon the        
,colours like so many black ,lines drawn
 over them1 or like long and slender    
dark ,shadows cast upon them4 ,i might  
have drawn black ,lines with a ,pen1 but
 the ,threds were smaller and better    
defined4 ,this ,paper thus coloured and 
lined ,i set against a ,wall            
perpendicularly to the ,horizon1 so that
 one of the ,colours might stand to the 
,right ,hand1 and the other to the      
,left4 ,close before the ,paper1 at the 
,confine of the ,colours below1 ,i      
placed a ,candle to illuminate the      
,paper strongly3 ,for the ,experiment   

was tried in the ,night4 ,the ,flame of 
the ,candle reached up to the lower edge
 of the ,paper1 or a very little higher4
 ,then at the distance of six ,feet1 and
 one or two ,inches from the ,paper upon
 the ,floor ,i erected a ,glass ,lens   
four ,inches and a quarter broad1 which 
might collect the ,rays coming from the 
several ,points of the ,paper1 and make 
them converge towards so many other     
,points at the same distance of six     
,feet1 and one or two ,inches on the    
other side of the ,lens1 and so form the
 ,image of the coloured ,paper upon a   
white ,paper placed there1 after the    
same manner that a ,lens at a ,hole in a
 ,window casts the ,images of ,objects  
abroad upon a ,sheet of white ,paper in 
a dark ,room4 ,the aforesaid white      
,paper1 erected perpendicular to the    
,horizon1 and to the ,rays which fell   
upon it from the ,lens1 ,i moved        
sometimes towards the ,lens1 sometimes  
from it1 to find the ,places where the  
,images of the blue and red ,parts of   

the coloured ,paper appeared most       
distinct4 ,those ,places ,i easily knew 
by the ,images of the black ,lines which
 ,i had made by winding the ,silk about 
the ,paper4 ,for the ,images of those   
fine and slender ,lines 7which by reason
 of their ,blackness were like ,shadows 
on the ,colours7 were confused and      
scarce visible1 unless when the ,colours
 on either side of each ,line were      
terminated most distinctly1 ,noting     
therefore1 as diligently as ,i could1   
the ,places where the ,images of the red
 and blue halfs of the coloured ,paper  
appeared most distinct1 ,i found that   
where the red half of the ,paper        
appeared distinct1 the blue half        
appeared confused1 so that the black    
,lines drawn upon it could scarce be    
seen2 and on the contrary1 where the    
blue half appeared most distinct1 the   
red half appeared confused1 so that the 
black ,lines upon it were scarce        
visible4 ,and between the two ,places   
where these ,images appeared distinct   

there was the distance of an ,inch and a
 half2 the distance of the white ,paper 
from the ,lens1 when the ,image of the  
red half of the coloured ,paper appeared
 most distinct1 being greater by an     
,inch and an half than the distance of  
the same white ,paper from the ,lens1   
when the ,image of the blue half        
appeared most distinct4 ,in like        
,incidences therefore of the blue and   
red upon the ,lens1 the blue was        
refracted more by the ,lens than the    
red1 so as to converge sooner by an     
,inch and a half1 and therefore is more 
refrangible4  ,illustration4 ,in the    
twelfth ,figure 7p4 #bg71 ,,de signifies
 the coloured ,paper1 ,,dg the blue     
half1 ,,fe the red half1 ,,mn the ,lens1
 ,,hj the white ,paper in that ,place   
where the red half with its black ,lines
 appeared distinct1 and hi the same     
,paper in that ,place where the blue    
half appeared distinct4 ,the ,place hi  
was nearer to the ,lens ,,mn than the   
,place ,,hj by an ,inch and an half4    

,scholium4 ,the same ,things succeed1   
notwithstanding that some of the        
,circumstances be varied2 as in the     
first ,experiment when the ,prism and   
,paper are any ways inclined to the     
,horizon1 and in both when coloured     
,lines are drawn upon very black ,paper4
 ,but in the ,description of these      
,experiments1 ,i have set down such     
,circumstances1 by which either the     
,phaenomenon might be render'd more     
conspicuous1 or a ,novice might more    
easily try them1 or by which ,i did try 
them only4 ,the same ,thing1 ,i have    
often done in the following             
,experiments3 ,concerning all which1    
this one ,admonition may suffice4 ,now  
from these ,experiments it follows not1 
that all the ,light of the blue is more 
refrangible than all the ,light of the  
red3 ,for both ,lights are mixed of     
,rays differently refrangible1 so that  
in the red there are some ,rays not less
 refrangible than those of the blue1 and
 in the blue there are some ,rays not   

more refrangible than those of the red3 
,but these ,rays1 in proportion to the  
whole ,light1 are but few1 and serve to 
diminish the ,event of the ,experiment1 
but are not able to destroy it4 ,for1 if
 the red and blue ,colours were more    
dilute and weak1 the distance of the    
,images would be less than an ,inch and 
a half2 and if they were more intense   
and full1 that distance would be        
greater1 as will appear hereafter4      
,these ,experiments may suffice for the 
,colours of ,natural ,bodies4 ,for in   
the ,colours made by the ,refraction of 
,prisms1 this ,proposition will appear  
by the ,experiments which are now to    
follow in the next ,proposition4        
,,prop4 ,,ii4 ,,theor4 ,,ii4  ,the      
,light of the ,sun consists of ,rays    
differently ,refrangible4  ,the ,,proof 
by ,experiments4  ,illustration3 ,,fig4 
#ab4  ,illustration3 ,,fig4 #ac4        
,exper4 #c4  ,in a very dark ,chamber1  
at a round ,hole1 about one third ,part 
of an ,inch broad1 made in the ,shut of 

a ,window1 ,i placed a ,glass ,prism1   
whereby the ,beam of the ,sun's ,light1 
which came in at that ,hole1 might be   
refracted upwards toward the opposite   
,wall of the ,chamber1 and there form a 
colour'd ,image of the ,sun4 ,the ,axis 
of the ,prism 7that is1 the ,line       
passing through the middle of the ,prism
 from one end of it to the other end    
parallel to the edge of the ,refracting 
,angle7 was in this and the following   
,experiments perpendicular to the       
incident ,rays4 ,about this ,axis ,i    
turned the ,prism slowly1 and saw the   
refracted ,light on the ,wall1 or       
coloured ,image of the ,sun1 first to   
descend1 and then to ascend4 ,between   
the ,descent and ,ascent1 when the      
,image seemed ,stationary1 ,i stopp'd   
the ,prism1 and fix'd it in that        
,posture1 that it should be moved no    
more4 ,for in that ,posture the         
,refractions of the ,light at the two   
,sides of the refracting ,angle1 that   
is1 at the ,entrance of the ,rays into  

the ,prism1 and at their going out of   
it1 were equal to one another4,c ,so    
also in other ,experiments1 as often as 
,i would have the ,refractions on both  
sides the ,prism to be equal to one     
another1 ,i noted the ,place where the  
,image of the ,sun formed by the        
refracted ,light stood still between its
 two contrary ,motions1 in the common   
,period of its ,progress and ,regress2  
and when the ,image fell upon that      
,place1 ,i made fast the ,prism4 ,and in
 this ,posture1 as the most convenient1 
it is to be understood that all the     
,prisms are placed in the following     
,experiments1 unless where some other   
,posture is described4 ,the ,prism      
therefore being placed in this ,posture1
 ,i let the refracted ,light fall       
perpendicularly upon a ,sheet of white  
,paper at the opposite ,wall of the     
,chamber1 and observed the ,figure and  
,dimensions of the ,solar ,image formed 
on the ,paper by that ,light4 ,this     
,image was ,oblong and not ,oval1 but   

terminated with two ,rectilinear and    
,parallel ,sides1 and two ,semicircular 
,ends4 ,on its ,sides it was bounded    
pretty distinctly1 but on its ,ends very
 confusedly and indistinctly1 the ,light
 there decaying and vanishing by        
degrees4 ,the ,breadth of this ,image   
answered to the ,sun's ,diameter1 and   
was about two ,inches and the eighth    
,part of an ,inch1 including the        
,penumbra4 ,for the ,image was eighteen 
,feet and an half distant from the      
,prism1 and at this distance that       
,breadth1 if diminished by the ,diameter
 of the ,hole in the ,window-shut1 that 
is by a quarter of an ,inch1 subtended  
an ,angle at the ,prism of about half a 
,degree1 which is the ,sun's apparent   
,diameter4 ,but the ,length of the      
,image was about ten ,inches and a      
quarter1 and the ,length of the         
,rectilinear ,sides about eight ,inches2
 and the refracting ,angle of the       
,prism1 whereby so great a ,length was  
made1 was #fd degrees4 ,with a less     

,angle the ,length of the ,image was    
less1 the ,breadth remaining the same4  
,if the ,prism was turned about its     
,axis that way which made the ,rays     
emerge more obliquely out of the second 
refracting ,surface of the ,prism1 the  
,image soon became an ,inch or two      
longer1 or more2 and if the ,prism was  
turned about the contrary way1 so as to 
make the ,rays fall more obliquely on   
the first refracting ,surface1 the      
,image soon became an ,inch or two      
shorter4 ,and therefore in trying this  
,experiment1 ,i was as curious as ,i    
could be in placing the ,prism by the   
above-mention'd ,rule exactly in such a 
,posture1 that the ,refractions of the  
,rays at their ,emergence out of the    
,prism might be equal to that at their  
,incidence on it4 ,this ,prism had some 
,veins running along within the ,glass  
from one end to the other1 which        
scattered some of the ,sun's ,light     
irregularly1 but had no sensible ,effect
 in increasing the ,length of the       

coloured ,spectrum4 ,for ,i tried the   
same ,experiment with other ,prisms with
 the same ,success4 ,and particularly   
with a ,prism which seemed free from    
such ,veins1 and whose refracting ,angle
 was #fb-a_/b ,degrees1 ,i found the    
,length of the ,image #i-c_/d or #aj    
,inches at the distance of #ah-a_/b     
,feet from the ,prism1 the ,breadth of  
the ,hole in the ,window-shut being     
#a_/d of an ,inch1 as before4 ,and      
because it is easy to commit a ,mistake 
in placing the ,prism in its due        
,posture1 ,i repeated the ,experiment   
four or five ,times1 and always found   
the ,length of the ,image that which is 
set down above4 ,with another ,prism of 
clearer ,glass and better ,polish1 which
 seemed free from ,veins1 and whose     
refracting ,angle was #fc-a_/b ,degrees1
 the ,length of this ,image at the same 
distance of #ah-a_/b ,feet was also     
about #aj ,inches1 or #aj-a_/h4 ,beyond 
these ,measures for about a #a_/d or    
#a_/c of an ,inch at either end of the  

,spectrum the ,light of the ,clouds     
seemed to be a little tinged with red   
and violet1 but so very faintly1 that ,i
 suspected that ,tincture might either  
wholly1 or in great ,measure arise from 
some ,rays of the ,spectrum scattered   
irregularly by some ,inequalities in the
 ,substance and ,polish of the ,glass1  
and therefore ,i did not include it in  
these ,measures4 ,now the different     
,magnitude of the hole in the           
,window-shut1 and different thickness of
 the ,prism where the ,rays passed      
through it1 and different inclinations  
of the ,prism to the ,horizon1 made no  
sensible changes in the length of the   
,image4 ,neither did the different      
matter of the ,prisms make any3 for in a
 ,vessel made of polished ,plates of    
,glass cemented together in the shape of
 a ,prism and filled with ,water1 there 
is the like ,success of the ,experiment 
according to the quantity of the        
,refraction4 ,it is farther to be       
observed1 that the ,rays went on in     

right ,lines from the ,prism to the     
,image1 and therefore at their very     
going out of the ,prism had all that    
,inclination to one another from which  
the length of the ,image proceeded1 that
 is1 the ,inclination of more than two  
degrees and an half4 ,and yet according 
to the ,laws of ,opticks vulgarly       
received1 they could not possibly be so 
much inclined to one another4,d ,for let
 ,,eg ,fig4 #ac4 7p4 #bg7 represent the 
,window-shut1 ,f the hole made therein  
through which a beam of the ,sun's      
,light was transmitted into the darkened
 ,chamber1 and ,,abc a ,triangular      
,imaginary ,plane whereby the ,prism is 
feigned to be cut transversely through  
the middle of the ,light4 ,or if you    
please1 let ,,abc represent the ,prism  
it self1 looking directly towards the   
,spectator's ,eye with its nearer end3  
,and let ,,xy be the ,sun1 ,,mn the     
,paper upon which the ,solar ,image or  
,spectrum is cast1 and ,,pt the ,image  
it self whose sides towards v and w are 

,rectilinear and ,parallel1 and ends    
towards ,p and ,t ,semicircular4 ,,ykhp 
and ,,xljt are two ,rays1 the first of  
which comes from the lower part of the  
,sun to the higher part of the ,image1  
and is refracted in the ,prism at ,k and
 ,h1 and the latter comes from the      
higher part of the ,sun to the lower    
part of the ,image1 and is refracted at 
,l and ,j4 ,since the ,refractions on   
both sides the ,prism are equal to one  
another1 that is1 the ,refraction at ,k 
equal to the ,refraction at ,j1 and the 
,refraction at ,l equal to the          
,refraction at ,h1 so that the          
,refractions of the incident ,rays at ,k
 and ,l taken together1 are equal to the
 ,refractions of the emergent ,rays at  
,h and ,j taken together3 it follows by 
adding equal things to equal things1    
that the ,refractions at ,k and ,h taken
 together1 are equal to the ,refractions
 at ,j and ,l taken together1 and       
therefore the two ,rays being equally   
refracted1 have the same ,inclination to

 one another after ,refraction which    
they had before2 that is1 the           
,inclination of half a ,degree answering
 to the ,sun's ,diameter4 ,for so great 
was the inclination of the ,rays to one 
another before ,refraction4 ,so then1   
the length of the ,image ,,pt would by  
the ,rules of ,vulgar ,opticks subtend  
an ,angle of half a ,degree at the      
,prism1 and by ,consequence be equal to 
the breadth vw2 and therefore the ,image
 would be round4 ,thus it would be were 
the two ,rays ,,xljt and ,,ykhp1 and all
 the rest which form the ,image ,pw,tv1 
alike refrangible4 ,and therefore seeing
 by ,experience it is found that the    
,image is not round1 but about five     
times longer than broad1 the ,rays which
 going to the upper end ,p of the ,image
 suffer the greatest ,refraction1 must  
be more refrangible than those which go 
to the lower end ,t1 unless the         
,inequality of ,refraction be casual4   
,this ,image or ,spectrum ,,pt was      
coloured1 being red at its least        

refracted end ,t1 and violet at its most
 refracted end ,p1 and yellow green and 
blue in the intermediate ,spaces4 ,which
 agrees with the first ,proposition1    
that ,lights which differ in ,colour1 do
 also differ in ,refrangibility4 ,the   
length of the ,image in the foregoing   
,experiments1 ,i measured from the      
faintest and outmost red at one end1 to 
the faintest and outmost blue at the    
other end1 excepting only a little      
,penumbra1 whose breadth scarce exceeded
 a quarter of an ,inch1 as was said     
above4  ,exper4 #d4 ,in the ,sun's ,beam
 which was propagated into the ,room    
through the hole in the ,window-shut1 at
 the distance of some ,feet from the    
hole1 ,i held the ,prism in such a      
,posture1 that its ,axis might be       
perpendicular to that ,beam4 ,then ,i   
looked through the ,prism upon the hole1
 and turning the ,prism to and fro about
 its ,axis1 to make the ,image of the   
,hole ascend and descend1 when between  
its two contrary ,motions it seemed     

,stationary1 ,i stopp'd the ,prism1 that
 the ,refractions of both sides of the  
refracting ,angle might be equal to each
 other1 as in the former ,experiment4   
,in this situation of the ,prism viewing
 through it the said ,hole1 ,i observed 
the length of its refracted ,image to be
 many times greater than its breadth1   
and that the most refracted part thereof
 appeared violet1 the least refracted   
red1 the middle parts blue1 green and   
yellow in order4 ,the same thing        
happen'd when ,i removed the ,prism out 
of the ,sun's ,light1 and looked through
 it upon the hole shining by the ,light 
of the ,clouds beyond it4 ,and yet if   
the ,refraction were done regularly     
according to one certain ,proportion of 
the ,sines of ,incidence and ,refraction
 as is vulgarly supposed1 the refracted 
,image ought to have appeared round4    
,so then1 by these two ,experiments it  
appears1 that in ,equal ,incidences     
there is a considerable inequality of   
,refractions4 ,but whence this          

inequality arises1 whether it be that   
some of the incident ,rays are refracted
 more1 and others less1 constantly1 or  
by chance1 or that one and the same ,ray
 is by ,refraction disturbed1 shatter'd1
 dilated1 and as it were split and      
spread into many diverging ,rays1 as    
,grimaldo supposes1 does not yet appear 
by these ,experiments1 but will appear  
by those that follow4  ,exper4 #e4      
,considering therefore1 that if in the  
third ,experiment the ,image of the ,sun
 should be drawn out into an oblong     
,form1 either by a ,dilatation of every 
,ray1 or by any other casual inequality 
of the ,refractions1 the same oblong    
,image would by a second ,refraction    
made sideways be drawn out as much in   
breadth by the like ,dilatation of the  
,rays1 or other casual inequality of the
 ,refractions sideways1 ,i tried what   
would be the ,effects of such a second  
,refraction4 ,for this end ,i ordered   
all things as in the third ,experiment1 
and then placed a second ,prism         

immediately after the first in a cross  
,position to it1 that it might again    
refract the beam of the ,sun's ,light   
which came to it through the first      
,prism4 ,in the first ,prism this beam  
was refracted upwards1 and in the second
 sideways4 ,and ,i found that by the    
,refraction of the second ,prism1 the   
breadth of the ,image was not increased1
 but its superior part1 which in the    
first ,prism suffered the greater       
,refraction1 and appeared violet and    
blue1 did again in the second ,prism    
suffer a greater ,refraction than its   
inferior part1 which appeared red and   
yellow1 and this without any ,dilatation
 of the ,image in breadth4              
,illustration3 ,,fig4 #ad               
,illustration4 ,let ,s ,fig4 #ad1 #ae4  
represent the ,sun1 ,f the hole in the  
,window1 ,,abc the first ,prism1 ,,dh   
the second ,prism1 ,y the round ,image  
of the ,sun made by a direct beam of    
,light when the ,prisms are taken away1 
,,pt the oblong ,image of the ,sun made 

by that beam passing through the first  
,prism alone1 when the second ,prism is 
taken away1 and pt the ,image made by   
the cross ,refractions of both ,prisms  
together4 ,now if the ,rays which tend  
towards the several ,points of the round
 ,image ,y were dilated and spread by   
the ,refraction of the first ,prism1 so 
that they should not any longer go in   
single ,lines to single ,points1 but    
that every ,ray being split1 shattered1 
and changed from a ,linear ,ray to a    
,superficies of ,rays diverging from the
 ,point of ,refraction1 and lying in the
 ,plane of the ,angles of ,incidence and
 ,refraction1 they should go in those   
,planes to so many ,lines reaching      
almost from one end of the ,image ,,pt  
to the other1 and if that ,image should 
thence become oblong3 those ,rays and   
their several parts tending towards the 
several ,points of the ,image ,,pt ought
 to be again dilated and spread sideways
 by the transverse ,refraction of the   
second ,prism1 so as to compose a four  

square ,image1 such as is represented at
 ,greek3 pt4 ,for the better            
understanding of which1 let the ,image  
,,pt be distinguished into five equal   
parts ,,pqk1 ,,kqrl1 ,,lrsm1 ,,msvn1    
,,nvt4 ,and by the same irregularity    
that the orbicular ,light ,y is by the  
,refraction of the first ,prism dilated 
and drawn out into a long ,image ,,pt1  
the ,light ,,pqk which takes up a space 
of the same length and breadth with the 
,light ,y ought to be by the ,refraction
 of the second ,prism dilated and drawn 
out into the long ,image ,greek3 pqkp1  
and the ,light ,,kqrl into the long     
,image kqrl1 and the ,lights ,,lrsm1    
,,msvn1 ,,nvt1 into so many other long  
,images lrsm1 msvn1 nvt,greek3 t2 and   
all these long ,images would compose the
 four square ,images ,greek3 pt4 ,thus  
it ought to be were every ,ray dilated  
by ,refraction1 and spread into a       
triangular ,superficies of ,rays        
diverging from the ,point of            
,refraction4 ,for the second ,refraction

 would spread the ,rays one way as much 
as the first doth another1 and so dilate
 the ,image in breadth as much as the   
first doth in length4 ,and the same     
thing ought to happen1 were some rays   
casually refracted more than others4    
,but the ,event is otherwise4 ,the      
,image ,,pt was not made broader by the 
,refraction of the second ,prism1 but   
only became oblique1 as 'tis represented
 at pt1 its upper end ,p being by the   
,refraction translated to a greater     
distance than its lower end ,t4 ,so then
 the ,light which went towards the upper
 end ,p of the ,image1 was 7at equal    
,incidences7 more refracted in the      
second ,prism1 than the ,light which    
tended towards the lower end ,t1 that is
 the blue and violet1 than the red and  
yellow2 and therefore was more          
refrangible4 ,the same ,light was by the
 ,refraction of the first ,prism        
translated farther from the place ,y to 
which it tended before ,refraction2 and 
therefore suffered as well in the first 

,prism as in the second a greater       
,refraction than the rest of the ,light1
 and by consequence was more refrangible
 than the rest1 even before its         
incidence on the first ,prism4          
,sometimes ,i placed a third ,prism     
after the second1 and sometimes also a  
fourth after the third1 by all which the
 ,image might be often refracted        
sideways3 but the ,rays which were more 
refracted than the rest in the first    
,prism were also more refracted in all  
the rest1 and that without any          
,dilatation of the ,image sideways3 and 
therefore those ,rays for their         
constancy of a greater ,refraction are  
deservedly reputed more refrangible4    
,illustration3 ,,fig4 #ae  ,but that the
 meaning of this ,experiment may more   
clearly appear1 it is to be considered  
that the ,rays which are equally        
refrangible do fall upon a ,circle      
answering to the ,sun's ,disque4 ,for   
this was proved in the third            
,experiment4 ,by a ,circle ,i understand

 not here a perfect geometrical ,circle1
 but any orbicular ,figure whose length 
is equal to its breadth1 and which1 as  
to ,sense1 may seem circular4 ,let      
therefore ,,ag in ,fig4 #ae4 represent  
the ,circle which all the most          
refrangible ,rays propagated from the   
whole ,disque of the ,sun1 would        
illuminate and paint upon the opposite  
,wall if they were alone2 ,,el the      
,circle which all the least refrangible 
,rays would in like manner illuminate   
and paint if they were alone2 ,,bh1     
,,cj1 ,,dk1 the ,circles which so many  
intermediate sorts of ,rays would       
successively paint upon the ,wall1 if   
they were singly propagated from the    
,sun in successive order1 the rest being
 always intercepted2 and conceive that  
there are other intermediate ,circles   
without ,number1 which innumerable other
 intermediate sorts of ,rays would      
successively paint upon the ,wall if the
 ,sun should successively emit every    
sort apart4 ,and seeing the ,sun emits  

all these sorts at once1 they must all  
together illuminate and paint           
innumerable equal ,circles1 of all      
which1 being according to their degrees 
of ,refrangibility placed in order in a 
continual ,series1 that oblong ,spectrum
 ,,pt is composed which ,i described in 
the third ,experiment4 ,now if the      
,sun's circular ,image ,y in ,fig4 #ae4 
which is made by an unrefracted beam of 
,light was by any ,dilation of the      
single ,rays1 or by any other           
irregularity in the ,refraction of the  
first ,prism1 converted into the oblong 
,spectrum1 ,,pt3 then ought every       
,circle ,,ag1 ,,bh1 ,,cj1 c4 in that    
,spectrum1 by the cross ,refraction of  
the second ,prism again dilating or     
otherwise scattering the ,rays as       
before1 to be in like manner drawn out  
and transformed into an oblong ,figure1 
and thereby the breadth of the ,image   
,,pt would be now as much augmented as  
the length of the ,image ,y was before  
by the ,refraction of the first ,prism2 

and thus by the ,refractions of both    
,prisms together would be formed a four 
square ,figure p,greek3 pt,greek3 t1 as 
,i described above4 ,wherefore since the
 breadth of the ,spectrum ,,pt is not   
increased by the ,refraction sideways1  
it is certain that the ,rays are not    
split or dilated1 or otherways          
irregularly scatter'd by that           
,refraction1 but that every ,circle is  
by a regular and uniform ,refraction    
translated entire into another ,place1  
as the ,circle ,,ag by the greatest     
,refraction into the place ag1 the      
,circle ,,bh by a less ,refraction into 
the place bh1 the ,circle ,,cj by a     
,refraction still less into the place   
ci1 and so of the rest2 by which means a
 new ,spectrum pt inclined to the former
 ,,pt is in like manner composed of     
,circles lying in a right ,line2 and    
these ,circles must be of the same      
bigness with the former1 because the    
breadths of all the ,spectrums ,y1 ,,pt 
and pt at equal distances from the      

,prisms are equal4  ,i considered       
farther1 that by the breadth of the hole
 ,f through which the ,light enters into
 the dark ,chamber1 there is a ,penumbra
 made in the ,circuit of the ,spectrum  
,y1 and that ,penumbra remains in the   
rectilinear ,sides of the ,spectrums    
,,pt and pt4 ,i placed therefore at that
 hole a ,lens or ,object-glass of a     
,telescope which might cast the ,image  
of the ,sun distinctly on ,y without any
 ,penumbra at all1 and found that the   
,penumbra of the rectilinear ,sides of  
the oblong ,spectrums ,,pt and pt was   
also thereby taken away1 so that those  
,sides appeared as distinctly defined as
 did the ,circumference of the first    
,image ,y4 ,thus it happens if the      
,glass of the ,prisms be free from      
,veins1 and their sides be accurately   
plane and well polished without those   
numberless ,waves or ,curles which      
usually arise from ,sand-holes a little 
smoothed in polishing with ,putty4 ,if  
the ,glass be only well polished and    

free from ,veins1 and the ,sides not    
accurately plane1 but a little ,convex  
or ,concave1 as it frequently happens2  
yet may the three ,spectrums ,y1 ,,pt   
and pt want ,penumbras1 but not in equal
 distances from the ,prisms4 ,now from  
this want of ,penumbras1 ,i knew more   
certainly that every one of the ,circles
 was refracted according to some most   
regular1 uniform and constant ,law4 ,for
 if there were any irregularity in the  
,refraction1 the right ,lines ,,ae and  
,,gl1 which all the ,circles in the     
,spectrum ,,pt do touch1 could not by   
that ,refraction be translated into the 
,lines ae and gl as distinct and        
straight as they were before1 but there 
would arise in those translated ,lines  
some ,penumbra or ,crookedness or       
,undulation1 or other sensible          
,perturbation contrary to what is found 
by ,experience4 ,whatsoever ,penumbra or
 ,perturbation should be made in the    
,circles by the cross ,refraction of the
 second ,prism1 all that ,penumbra or   

,perturbation would be conspicuous in   
the right ,lines ae and gl which touch  
those ,circles4 ,and therefore since    
there is no such ,penumbra or           
,perturbation in those right ,lines1    
there must be none in the ,circles4     
,since the distance between those       
,tangents or breadth of the ,spectrum is
 not increased by the ,refractions1 the 
,diameters of the ,circles are not      
increased thereby4 ,since those         
,tangents continue to be right ,lines1  
every ,circle which in the first ,prism 
is more or less refracted1 is exactly in
 the same proportion more or less       
refracted in the second4 ,and seeing all
 these things continue to succeed after 
the same manner when the ,rays are again
 in a third ,prism1 and again in a      
fourth refracted sideways1 it is evident
 that the ,rays of one and the same     
,circle1 as to their degree of          
,refrangibility1 continue always uniform
 and homogeneal to one another1 and that
 those of several ,circles do differ in 

degree of ,refrangibility1 and that in  
some certain and constant ,proportion4  
,which is the thing ,i was to prove4    
,there is yet another ,circumstance or  
two of this ,experiment by which it     
becomes still more plain and convincing4
 ,let the second ,prism ,,dh in ,fig4   
#af4 be placed not immediately after the
 first1 but at some distance from it2   
suppose in the mid-way between it and   
the ,wall on which the oblong ,spectrum 
,,pt is cast1 so that the ,light from   
the first ,prism may fall upon it in the
 form of an oblong ,spectrum ,greek3 pt 
parallel to this second ,prism1 and be  
refracted sideways to form the oblong   
,spectrum pt upon the ,wall4 ,and you   
will find as before1 that this ,spectrum
 pt is inclined to that ,spectrum ,,pt1 
which the first ,prism forms alone      
without the second2 the blue ends ,p and
 p being farther distant from one       
another than the red ones ,t and t1 and 
by consequence that the ,rays which go  
to the blue end ,greek3 p of the ,image 

,greek3 pt1 and which therefore suffer  
the greatest ,refraction in the first   
,prism1 are again in the second ,prism  
more refracted than the rest4           
,illustration3 ,,fig4 #af4              
,illustration3 ,,fig4 #ag4  ,the same   
thing ,i try'd also by letting the      
,sun's ,light into a dark ,room through 
two little round holes ,f and ,greek3 ph
 in ,fig4 #ag4 made in the ,window1 and 
with two parallel ,prisms ,,abc and     
,greek3 abg placed at those holes 7one  
at each7 refracting those two beams of  
,light to the opposite ,wall of the     
,chamber1 in such manner that the two   
colour'd ,images ,,pt and ,,mn which    
they there painted were joined end to   
end and lay in one straight ,line1 the  
red end ,t of the one touching the blue 
end ,m of the other4 ,for if these two  
refracted ,beams were again by a third  
,prism ,,dh placed cross to the two     
first1 refracted sideways1 and the      
,spectrums thereby translated to some   
other part of the ,wall of the ,chamber1

 suppose the ,spectrum ,,pt to pt and   
the ,spectrum ,,mn to mn1 these         
translated ,spectrums pt and mn would   
not lie in one straight ,line with their
 ends contiguous as before1 but be      
broken off from one another and become  
parallel1 the blue end m of the ,image  
mn being by a greater ,refraction       
translated farther from its former place
 ,,mt1 than the red end t of the other  
,image pt from the same place ,,mt2     
which puts the ,proposition past        
,dispute4 ,and this happens whether the 
third ,prism ,,dh be placed immediately 
after the two first1 or at a great      
distance from them1 so that the ,light  
refracted in the two first ,prisms be   
either white and circular1 or coloured  
and oblong when it falls on the third4  
,exper4 #f4 ,in the middle of two thin  
,boards ,i made round holes a third part
 of an ,inch in diameter1 and in the    
,window-shut a much broader hole being  
made to let into my darkned ,chamber a  
large ,beam of the ,sun's ,light2 ,i    

placed a ,prism behind the ,shut in that
 beam to refract it towards the opposite
 ,wall1 and close behind the ,prism ,i  
fixed one of the ,boards1 in such manner
 that the middle of the refracted ,light
 might pass through the hole made in it1
 and the rest be intercepted by the     
,board4 ,then at the distance of about  
twelve ,feet from the first ,board ,i   
fixed the other ,board in such manner   
that the middle of the refracted ,light 
which came through the hole in the first
 ,board1 and fell upon the opposite     
,wall1 might pass through the hole in   
this other ,board1 and the rest being   
intercepted by the ,board might paint   
upon it the coloured ,spectrum of the   
,sun4 ,and close behind this ,board ,i  
fixed another ,prism to refract the     
,light which came through the hole4     
,then ,i returned speedily to the first 
,prism1 and by turning it slowly to and 
fro about its ,axis1 ,i caused the      
,image which fell upon the second ,board
 to move up and down upon that ,board1  

that all its parts might successively   
pass through the hole in that ,board and
 fall upon the ,prism behind it4 ,and in
 the mean time1 ,i noted the places on  
the opposite ,wall to which that ,light 
after its ,refraction in the second     
,prism did pass2 and by the difference  
of the places ,i found that the ,light  
which being most refracted in the first 
,prism did go to the blue end of the    
,image1 was again more refracted in the 
second ,prism than the ,light which went
 to the red end of that ,image1 which   
proves as well the first ,proposition as
 the second4 ,and this happened whether 
the ,axis of the two ,prisms were       
parallel1 or inclined to one another1   
and to the ,horizon in any given        
,angles4  ,illustration4 ,let ,f in     
,fig4 #ah4 be the wide hole in the      
,window-shut1 through which the ,sun    
shines upon the first ,prism ,,abc1 and 
let the refracted ,light fall upon the  
middle of the ,board ,,de1 and the      
middle part of that ,light upon the hole

 ,g made in the middle part of that     
,board4 ,let this trajected part of that
 ,light fall again upon the middle of   
the second ,board de1 and there paint   
such an oblong coloured ,image of the   
,sun as was described in the third      
,experiment4 ,by turning the ,prism     
,,abc slowly to and fro about its ,axis1
 this ,image will be made to move up and
 down the ,board de1 and by this means  
all its parts from one end to the other 
may be made to pass successively through
 the hole g which is made in the middle 
of that ,board4 ,in the mean while      
another ,prism abc is to be fixed next  
after that hole g1 to refract the       
trajected ,light a second time4 ,and    
these things being thus ordered1 ,i     
marked the places ,m and ,n of the      
opposite ,wall upon which the refracted 
,light fell1 and found that whilst the  
two ,boards and second ,prism remained  
unmoved1 those places by turning the    
first ,prism about its ,axis were       
changed perpetually4 ,for when the lower

 part of the ,light which fell upon the 
second ,board de was cast through the   
hole g1 it went to a lower place ,m on  
the ,wall and when the higher part of   
that ,light was cast through the same   
hole g1 it went to a higher place ,n on 
the ,wall1 and when any intermediate    
part of the ,light was cast through that
 hole1 it went to some place on the     
,wall between ,m and ,n4 ,the unchanged 
,position of the holes in the ,boards1  
made the ,incidence of the ,rays upon   
the second ,prism to be the same in all 
cases4 ,and yet in that common          
,incidence some of the ,rays were more  
refracted1 and others less4 ,and those  
were more refracted in this ,prism1     
which by a greater ,refraction in the   
first ,prism were more turned out of the
 way1 and therefore for their ,constancy
 of being more refracted are deservedly 
called more refrangible4  ,illustration3
 ,,fig4 #ah4  ,illustration3 ,,fig4 #bj4
  ,exper4 #g4 ,at two holes made near   
one another in my ,window-shut ,i placed

 two ,prisms1 one at each1 which might  
cast upon the opposite ,wall 7after the 
manner of the third ,experiment7 two    
oblong coloured ,images of the ,sun4    
,and at a little distance from the ,wall
 ,i placed a long slender ,paper with   
straight and parallel edges1 and ordered
 the ,prisms and ,paper so1 that the red
 ,colour of one ,image might fall       
directly upon one half of the ,paper1   
and the violet ,colour of the other     
,image upon the other half of the same  
,paper2 so that the ,paper appeared of  
two ,colours1 red and violet1 much after
 the manner of the painted ,paper in the
 first and second ,experiments4 ,then   
with a black ,cloth ,i covered the ,wall
 behind the ,paper1 that no ,light might
 be reflected from it to disturb the    
,experiment1 and viewing the ,paper     
through a third ,prism held parallel to 
it1 ,i saw that half of it which was    
illuminated by the violet ,light to be  
divided from the other half by a greater
 ,refraction1 especially when ,i went a 

good way off from the ,paper4 ,for when 
,i viewed it too near at hand1 the two  
halfs of the ,paper did not appear fully
 divided from one another1 but seemed   
contiguous at one of their ,angles like 
the painted ,paper in the first         
,experiment4 ,which also happened when  
the ,paper was too broad4               
,illustration3 ,,fig4 #ai4  ,sometimes  
instead of the ,paper ,i used a white   
,thred1 and this appeared through the   
,prism divided into two parallel ,threds
 as is represented in the nineteenth    
,figure1 where ,,dg denotes the ,thred  
illuminated with violet ,light from ,d  
to ,e and with red ,light from ,f to ,g1
 and defg are the parts of the ,thred   
seen by ,refraction4 ,if one half of the
 ,thred be constantly illuminated with  
red1 and the other half be illuminated  
with all the ,colours successively1     
7which may be done by causing one of the
 ,prisms to be turned about its ,axis   
whilst the other remains unmoved7 this  
other half in viewing the ,thred through

 the ,prism1 will appear in a continual 
right ,line with the first half when    
illuminated with red1 and begin to be a 
little divided from it when illuminated 
with ,orange1 and remove farther from it
 when illuminated with yellow1 and still
 farther when with green1 and farther   
when with blue1 and go yet farther off  
when illuminated with ,indigo1 and      
farthest when with deep violet4 ,which  
plainly shews1 that the ,lights of      
several ,colours are more and more      
refrangible one than another1 in this   
,order of their ,colours1 red1 orange1  
yellow1 green1 blue1 indigo1 deep       
violet2 and so proves as well the first 
,proposition as the second4  ,i caused  
also the coloured ,spectrums ,,pt in    
,fig4 #ag4 and ,,mn made in a dark      
,chamber by the ,refractions of two     
,prisms to lie in a ,right ,line end to 
end1 as was described above in the fifth
 ,experiment1 and viewing them through a
 third ,prism held parallel to their    
,length1 they appeared no longer in a   

,right ,line1 but became broken from one
 another1 as they are represented at pt 
and mn1 the violet end m of the         
,spectrum mn being by a greater         
,refraction translated farther from its 
former ,place ,,mt than the red end t of
 the other ,spectrum pt4  ,i farther    
caused those two ,spectrums ,,pt in     
,fig4 #bj4 and ,,mn to become           
co-incident in an inverted ,order of    
their ,colours1 the red end of each     
falling on the violet end of the other1 
as they are represented in the oblong   
,figure ,,ptmn2 and then viewing them   
through a ,prism ,,dh held parallel to  
their ,length1 they appeared not        
co-incident1 as when view'd with the    
naked ,eye1 but in the form of two      
distinct ,spectrums pt and mn crossing  
one another in the middle after the     
manner of the ,letter ,x4 ,which shews  
that the red of the one ,spectrum and   
violet of the other1 which were         
co-incident at ,,pn and ,,mt1 being     
parted from one another by a greater    

,refraction of the violet to p and m    
than of the red to n and t1 do differ in
 degrees of ,refrangibility4  ,i        
illuminated also a little ,circular     
,piece of white ,paper all over with the
 ,lights of both ,prisms intermixed1 and
 when it was illuminated with the red of
 one ,spectrum1 and deep violet of the  
other1 so as by the ,mixture of those   
,colours to appear all over purple1 ,i  
viewed the ,paper1 first at a less      
distance1 and then at a greater1 through
 a third ,prism2 and as ,i went from the
 ,paper1 the refracted ,image thereof   
became more and more divided by the     
unequal ,refraction of the two mixed    
,colours1 and at length parted into two 
distinct ,images1 a red one and a violet
 one1 whereof the violet was farthest   
from the ,paper1 and therefore suffered 
the greatest ,refraction4 ,and when that
 ,prism at the ,window1 which cast the  
violet on the ,paper was taken away1 the
 violet ,image disappeared2 but when the
 other ,prism was taken away the red    

vanished2 which shews1 that these two   
,images were nothing else than the      
,lights of the two ,prisms1 which had   
been intermixed on the purple ,paper1   
but were parted again by their unequal  
,refractions made in the third ,prism1  
through which the ,paper was view'd4    
,this also was observable1 that if one  
of the ,prisms at the ,window1 suppose  
that which cast the violet on the       
,paper1 was turned about its ,axis to   
make all the ,colours in this order1    
violet1 indigo1 blue1 green1 yellow1    
orange1 red1 fall successively on the   
,paper from that ,prism1 the violet     
,image changed ,colour accordingly1     
turning successively to indigo1 blue1   
green1 yellow and red1 and in changing  
,colour came nearer and nearer to the   
red ,image made by the other ,prism1    
until when it was also red both ,images 
became fully co-incident4  ,i placed    
also two ,paper ,circles very near one  
another1 the one in the red ,light of   
one ,prism1 and the other in the violet 

,light of the other4 ,the ,circles were 
each of them an ,inch in diameter1 and  
behind them the ,wall was dark1 that the
 ,experiment might not be disturbed by  
any ,light coming from thence4 ,these   
,circles thus illuminated1 ,i viewed    
through a ,prism1 so held1 that the     
,refraction might be made towards the   
red ,circle1 and as ,i went from them   
they came nearer and nearer together1   
and at length became co-incident2 and   
afterwards when ,i went still farther   
off1 they parted again in a contrary    
,order1 the violet by a greater         
,refraction being carried beyond the    
red4  ,exper4 #h4 ,in ,summer1 when the 
,sun's ,light uses to be strongest1 ,i  
placed a ,prism at the ,hole of the     
,window-shut1 as in the third           
,experiment1 yet so that its ,axis might
 be parallel to the ,axis of the ,world1
 and at the opposite ,wall in the ,sun's
 refracted ,light1 ,i placed an open    
,book4 ,then going six ,feet and two    
,inches from the ,book1 ,i placed there 

the above-mentioned ,lens1 by which the 
,light reflected from the ,book might be
 made to converge and meet again at the 
distance of six ,feet and two ,inches   
behind the ,lens1 and there paint the   
,species of the ,book upon a ,sheet of  
white ,paper much after the manner of   
the second ,experiment4 ,the ,book and  
,lens being made fast1 ,i noted the     
,place where the ,paper was1 when the   
,letters of the ,book1 illuminated by   
the fullest red ,light of the ,solar    
,image falling upon it1 did cast their  
,species on that ,paper most distinctly3
 ,and then ,i stay'd till by the ,motion
 of the ,sun1 and consequent ,motion of 
his ,image on the ,book1 all the        
,colours from that red to the middle of 
the blue pass'd over those ,letters2 and
 when those ,letters were illuminated by
 that blue1 ,i noted again the ,place of
 the ,paper when they cast their        
,species most distinctly upon it3 ,and  
,i found that this last ,place of the   
,paper was nearer to the ,lens than its 

former ,place by about two ,inches and  
an half1 or two and three quarters4 ,so 
much sooner therefore did the ,light in 
the violet end of the ,image by a       
greater ,refraction converge and meet1  
than the ,light in the red end4 ,but in 
trying this1 the ,chamber was as dark as
 ,i could make it4 ,for1 if these       
,colours be diluted and weakned by the  
,mixture of any adventitious ,light1 the
 distance between the ,places of the    
,paper will not be so great4 ,this      
distance in the second ,experiment1     
where the ,colours of natural ,bodies   
were made use of1 was but an ,inch and  
an half1 by reason of the ,imperfection 
of those ,colours4 ,here in the ,colours
 of the ,prism1 which are manifestly    
more full1 intense1 and lively than     
those of natural ,bodies1 the distance  
is two ,inches and three quarters4 ,and 
were the ,colours still more full1 ,i   
question not but that the distance would
 be considerably greater4 ,for the      
coloured ,light of the ,prism1 by the   

interfering of the ,circles described in
 the second ,figure of the fifth        
,experiment1 and also by the ,light of  
the very bright ,clouds next the ,sun's 
,body intermixing with these ,colours1  
and by the ,light scattered by the      
,inequalities in the ,polish of the     
,prism1 was so very much compounded1    
that the ,species which those faint and 
dark ,colours1 the indigo and violet1   
cast upon the ,paper were not distinct  
enough to be well observed4  ,exper4 #i4
 ,a ,prism1 whose two ,angles at its    
,base were equal to one another1 and    
half right ones1 and the third a right  
one1 ,i placed in a ,beam of the ,sun's 
,light let into a dark ,chamber through 
a ,hole in the ,window-shut1 as in the  
third ,experiment4 ,and turning the     
,prism slowly about its ,axis1 until all
 the ,light which went through one of   
its ,angles1 and was refracted by it    
began to be reflected by its ,base1 at  
which till then it went out of the      
,glass1 ,i observed that those ,rays    

which had suffered the greatest         
,refraction were sooner reflected than  
the rest4 ,i conceived therefore1 that  
those ,rays of the reflected ,light1    
which were most refrangible1 did first  
of all by a total ,reflexion become more
 copious in that ,light than the rest1  
and that afterwards the rest also1 by a 
total ,reflexion1 became as copious as  
these4 ,to try this1 ,i made the        
reflected ,light pass through another   
,prism1 and being refracted by it to    
fall afterwards upon a ,sheet of white  
,paper placed at some distance behind   
it1 and there by that ,refraction to    
paint the usual ,colours of the ,prism4 
,and then causing the first ,prism to be
 turned about its ,axis as above1 ,i    
observed that when those ,rays1 which in
 this ,prism had suffered the greatest  
,refraction1 and appeared of a blue and 
violet ,colour began to be totally      
reflected1 the blue and violet ,light on
 the ,paper1 which was most refracted in
 the second ,prism1 received a sensible 

,increase above that of the red and     
yellow1 which was least refracted2 and  
afterwards1 when the rest of the ,light 
which was green1 yellow1 and red1 began 
to be totally reflected in the first    
,prism1 the ,light of those ,colours on 
the ,paper received as great an         
,increase as the violet and blue had    
done before4 ,whence 'tis manifest1 that
 the ,beam of ,light reflected by the   
,base of the ,prism1 being augmented    
first by the more refrangible ,rays1 and
 afterwards by the less refrangible     
ones1 is compounded of ,rays differently
 refrangible4 ,and that all such        
reflected ,light is of the same ,nature 
with the ,sun's ,light before its       
,incidence on the ,base of the ,prism1  
no ,man ever doubted2 it being generally
 allowed1 that ,light by such           
,reflexions suffers no ,alteration in   
its ,modifications and ,properties4 ,i  
do not here take ,notice of any         
,refractions made in the sides of the   
first ,prism1 because the ,light enters 

it perpendicularly at the first side1   
and goes out perpendicularly at the     
second side1 and therefore suffers none4
 ,so then1 the ,sun's incident ,light   
being of the same ,temper and           
,constitution with his emergent ,light1 
and the last being compounded of ,rays  
differently refrangible1 the first must 
be in like manner compounded4           
,illustration3 ,,fig4 #ba4              
,illustration4 ,in the twenty-first     
,figure1 ,,abc is the first ,prism1 ,,bc
 its ,base1 ,b and ,c its equal ,angles 
at the ,base1 each of #de ,degrees1 ,a  
its rectangular ,vertex1 ,,fm a beam of 
the ,sun's ,light let into a dark ,room 
through a hole ,f one third part of an  
,inch broad1 ,m its ,incidence on the   
,base of the ,prism1 ,,mg a less        
refracted ,ray1 ,,mh a more refracted   
,ray1 ,,mn the beam of ,light reflected 
from the ,base1 ,,vxy the second ,prism 
by which this beam in passing through it
 is refracted1 ,nt the less refracted   
,light of this beam1 and ,np the more   

refracted part thereof4 ,when the first 
,prism ,,abc is turned about its ,axis  
according to the order of the ,letters  
,,abc1 the ,rays ,,mh emerge more and   
more obliquely out of that ,prism1 and  
at length after their most oblique      
,emergence are reflected towards ,n1 and
 going on to p do increase the ,number  
of the ,rays ,np4 ,afterwards by        
continuing the ,motion of the first     
,prism1 the ,rays ,,mg are also         
reflected to ,n and increase the number 
of the ,rays ,nt4 ,and therefore the    
,light ,,mn admits into its             
,composition1 first the more refrangible
 ,rays1 and then the less refrangible   
,rays1 and yet after this ,composition  
is of the same ,nature with the ,sun's  
immediate ,light ,,fm1 the ,reflexion of
 the specular ,base ,,bc causing no     
,alteration therein4  ,exper4 #aj4 ,two 
,prisms1 which were alike in ,shape1 ,i 
tied so together1 that their ,axis and  
opposite ,sides being parallel1 they    
composed a ,parallelopiped4 ,and1 the   

,sun shining into my dark ,chamber      
through a little hole in the            
,window-shut1 ,i placed that            
,parallelopiped in his beam at some     
distance from the hole1 in such a       
,posture1 that the ,axes of the ,prisms 
might be perpendicular to the incident  
,rays1 and that those ,rays being       
incident upon the first ,side of one    
,prism1 might go on through the two     
contiguous ,sides of both ,prisms1 and  
emerge out of the last ,side of the     
second ,prism4 ,this ,side being        
parallel to the first ,side of the first
 ,prism1 caused the emerging ,light to  
be parallel to the incident4 ,then1     
beyond these two ,prisms ,i placed a    
third1 which might refract that emergent
 ,light1 and by that ,refraction cast   
the usual ,colours of the ,prism upon   
the opposite ,wall1 or upon a sheet of  
white ,paper held at a convenient       
,distance behind the ,prism for that    
refracted ,light to fall upon it4 ,after
 this ,i turned the ,parallelopiped     

about its ,axis1 and found that when the
 contiguous ,sides of the two ,prisms   
became so oblique to the incident ,rays1
 that those ,rays began all of them to  
be reflected1 those ,rays which in the  
third ,prism had suffered the greatest  
,refraction1 and painted the ,paper with
 violet and blue1 were first of all by a
 total ,reflexion taken out of the      
transmitted ,light1 the rest remaining  
and on the ,paper painting their        
,colours of green1 yellow1 orange and   
red1 as before2 and afterwards by       
continuing the ,motion of the two       
,prisms1 the rest of the ,rays also by a
 total ,reflexion vanished in order1    
according to their degrees of           
,refrangibility4 ,the ,light therefore  
which emerged out of the two ,prisms is 
compounded of ,rays differently         
refrangible1 seeing the more refrangible
 ,rays may be taken out of it1 while the
 less refrangible remain4 ,but this     
,light being trajected only through the 
parallel ,superficies of the two        

,prisms1 if it suffer'd any change by   
the ,refraction of one ,superficies it  
lost that ,impression by the contrary   
,refraction of the other ,superficies1  
and so being restor'd to its pristine   
,constitution1 became of the same       
,nature and ,condition as at first      
before its ,incidence on those ,prisms2 
and therefore1 before its ,incidence1   
was as much compounded of ,rays         
differently refrangible1 as afterwards4 
,illustration3 ,,fig4 #bb4              
,illustration4 ,in the twenty second    
,figure ,,abc and ,,bcd are the two     
,prisms tied together in the form of a  
,parallelopiped1 their ,sides ,,bc and  
,,cb being contiguous1 and their ,sides 
,,ab and ,,cd parallel4 ,and ,,hjk is   
the third ,prism1 by which the ,sun's   
,light propagated through the hole ,f   
into the dark ,chamber1 and there       
passing through those sides of the      
,prisms ,,ab1 ,,bc1 ,,cb and ,,cd1 is   
refracted at ,o to the white ,paper     
,,pt1 falling there partly upon ,p by a 

greater ,refraction1 partly upon ,t by a
 less ,refraction1 and partly upon ,r   
and other intermediate places by        
intermediate ,refractions4 ,by turning  
the ,parallelopiped ,,acbd about its    
,axis1 according to the order of the    
,letters ,a1 ,c1 ,d1 ,b1 at length when 
the contiguous ,planes ,,bc and ,,cb    
become sufficiently oblique to the ,rays
 ,,fm1 which are incident upon them at  
,m1 there will vanish totally out of the
 refracted ,light ,,opt1 first of all   
the most refracted ,rays ,,op1 7the rest
 ,,or and ,,ot remaining as before7 then
 the ,rays ,,or and other intermediate  
ones1 and lastly1 the least refracted   
,rays ,,ot4 ,for when the ,plane ,,bc   
becomes sufficiently oblique to the     
,rays incident upon it1 those ,rays will
 begin to be totally reflected by it    
towards ,n2 and first the most          
refrangible ,rays will be totally       
reflected 7as was explained in the      
preceding ,experiment7 and by           
,consequence must first disappear at ,p1

 and afterwards the rest as they are in 
order totally reflected to ,n1 they must
 disappear in the same order at ,r and  
,t4 ,so then the ,rays which at ,o      
suffer the greatest ,refraction1 may be 
taken out of the ,light ,,mo whilst the 
rest of the ,rays remain in it1 and     
therefore that ,light ,,mo is compounded
 of ,rays differently refrangible4 ,and 
because the ,planes ,,ab and ,,cd are   
parallel1 and therefore by equal and    
contrary ,refractions destroy one       
anothers ,effects1 the incident ,light  
,,fm must be of the same ,kind and      
,nature with the emergent ,light ,,mo1  
and therefore doth also consist of ,rays
 differently refrangible4 ,these two    
,lights ,,fm and ,,mo1 before the most  
refrangible ,rays are separated out of  
the emergent ,light ,,mo1 agree in      
,colour1 and in all other ,properties so
 far as my ,observation reaches1 and    
therefore are deservedly reputed of the 
same ,nature and ,constitution1 and by  
,consequence the one is compounded as   

well as the other4 ,but after the most  
refrangible ,rays begin to be totally   
reflected1 and thereby separated out of 
the emergent ,light ,,mo1 that ,light   
changes its ,colour from white to a     
dilute and faint yellow1 a pretty good  
orange1 a very full red successively1   
and then totally vanishes4 ,for after   
the most refrangible ,rays which paint  
the ,paper at ,p with a purple ,colour1 
are by a total ,reflexion taken out of  
the beam of ,light ,,mo1 the rest of the
 ,colours which appear on the ,paper at 
,r and ,t being mix'd in the ,light ,,mo
 compound there a faint yellow1 and     
after the blue and part of the green    
which appear on the ,paper between ,p   
and ,r are taken away1 the rest which   
appear between ,r and ,t 7that is the   
yellow1 orange1 red and a little green7 
being mixed in the beam ,,mo compound   
there an orange2 and when all the ,rays 
are by ,reflexion taken out of the beam 
,,mo1 except the least refrangible1     
which at ,t appear of a full red1 their 

,colour is the same in that beam ,,mo as
 afterwards at ,t1 the ,refraction of   
the ,prism ,,hjk serving only to        
separate the differently refrangible    
,rays1 without making any ,alteration in
 their ,colours1 as shall be more fully 
proved hereafter4 ,all which confirms as
 well the first ,proposition as the     
second4  ,scholium4 ,if this ,experiment
 and the former be conjoined and made   
one by applying a fourth ,prism ,,vxy in
 ,fig4 #bb4 to refract the reflected    
beam ,,mn towards tp1 the ,conclusion   
will be clearer4 ,for then the ,light   
,np which in the fourth ,prism is more  
refracted1 will become fuller and       
stronger when the ,light ,,op1 which in 
the third ,prism ,,hjk is more          
refracted1 vanishes at ,p2 and          
afterwards when the less refracted      
,light ,,ot vanishes at ,t1 the less    
refracted ,light ,nt will become        
increased whilst the more refracted     
,light at p receives no farther         
increase4 ,and as the trajected beam    

,,mo in vanishing is always of such a   
,colour as ought to result from the     
mixture of the ,colours which fall upon 
the ,paper ,,pt1 so is the reflected    
beam ,,mn always of such a ,colour as   
ought to result from the mixture of the 
,colours which fall upon the ,paper pt4 
,for when the most refrangible ,rays are
 by a total ,reflexion taken out of the 
beam ,,mo1 and leave that beam of an    
orange ,colour1 the ,excess of those    
,rays in the reflected ,light1 does not 
only make the violet1 indigo and blue at
 p more full1 but also makes the beam   
,,mn change from the yellowish ,colour  
of the ,sun's ,light1 to a pale white   
inclining to blue1 and afterward recover
 its yellowish ,colour again1 so soon as
 all the rest of the transmitted ,light 
,,mot is reflected4  ,now seeing that in
 all this variety of ,experiments1      
whether the ,trial be made in ,light    
reflected1 and that either from natural 
,bodies1 as in the first and second     
,experiment1 or specular1 as in the     

ninth2 or in ,light refracted1 and that 
either before the unequally refracted   
,rays are by diverging separated from   
one another1 and losing their whiteness 
which they have altogether1 appear      
severally of several ,colours1 as in the
 fifth ,experiment2 or after they are   
separated from one another1 and appear  
colour'd as in the sixth1 seventh1 and  
eighth ,experiments2 or in ,light       
trajected through parallel ,superficies1
 destroying each others ,effects1 as in 
the tenth ,experiment2 there are always 
found ,rays1 which at equal ,incidences 
on the same ,medium suffer unequal      
,refractions1 and that without any      
splitting or dilating of single ,rays1  
or contingence in the inequality of the 
,refractions1 as is proved in the fifth 
and sixth ,experiments4 ,and seeing the 
,rays which differ in ,refrangibility   
may be parted and sorted from one       
another1 and that either by ,refraction 
as in the third ,experiment1 or by      
,reflexion as in the tenth1 and then the

 several sorts apart at equal           
,incidences suffer unequal ,refractions1
 and those sorts are more refracted than
 others after ,separation1 which were   
more refracted before it1 as in the     
sixth and following ,experiments1 and if
 the ,sun's ,light be trajected through 
three or more cross ,prisms             
successively1 those ,rays which in the  
first ,prism are refracted more than    
others1 are in all the following ,prisms
 refracted more than others in the same 
,rate and ,proportion1 as appears by the
 fifth ,experiment2 it's manifest that  
the ,sun's ,light is an heterogeneous   
,mixture of ,rays1 some of which are    
constantly more refrangible than others1
 as was proposed4   ,,prop4 ,,iii4      
,,theor4 ,,iii4  ,the ,sun's ,light     
consists of ,rays differing in          
,reflexibility1 and those ,rays are more
 reflexible than others which are more  
refrangible4  ,this is manifest by the  
ninth and tenth ,experiments3 ,for in   
the ninth ,experiment1 by turning the   

,prism about its ,axis1 until the ,rays 
within it which in going out into the   
,air were refracted by its ,base1 became
 so oblique to that ,base1 as to begin  
to be totally reflected thereby2 those  
,rays became first of all totally       
reflected1 which before at equal        
,incidences with the rest had suffered  
the greatest ,refraction4 ,and the same 
thing happens in the ,reflexion made by 
the common ,base of the two ,prisms in  
the tenth ,experiment4   ,,prop4 ,,iv4  
,,prob4 ,i4  ,to separate from one      
another the heterogeneous ,rays of      
compound ,light4  ,illustration3 ,,fig4 
#bc4  ,the heterogeneous ,rays are in   
some measure separated from one another 
by the ,refraction of the ,prism in the 
third ,experiment1 and in the fifth     
,experiment1 by taking away the         
,penumbra from the rectilinear sides of 
the coloured ,image1 that ,separation in
 those very rectilinear sides or        
straight edges of the ,image becomes    
perfect4 ,but in all places between     

those rectilinear edges1 those          
innumerable ,circles there described1   
which are severally illuminated by      
homogeneal ,rays1 by interfering with   
one another1 and being every where      
commix'd1 do render the ,light          
sufficiently compound4 ,but if these    
,circles1 whilst their ,centers keep    
their ,distances and ,positions1 could  
be made less in ,diameter1 their        
interfering one with another1 and by    
,consequence the ,mixture of the        
heterogeneous ,rays would be            
proportionally diminish'd4 ,in the      
twenty third ,figure let ,,ag1 ,,bh1    
,,cj1 ,,dk1 ,,el1 ,,fm be the ,circles  
which so many sorts of ,rays flowing    
from the same disque of the ,sun1 do in 
the third ,experiment illuminate2 of all
 which and innumerable other            
intermediate ones lying in a continual  
,series between the two rectilinear and 
parallel edges of the ,sun's oblong     
,image ,,pt1 that ,image is compos'd1 as
 was explained in the fifth ,experiment4

 ,and let ag1 bh1 ci1 dk1 el1 fm be so  
many less ,circles lying in a like      
continual ,series between two parallel  
right ,lines af and gm with the same    
distances between their ,centers1 and   
illuminated by the same sorts of ,rays1 
that is the ,circle ag with the same    
sort by which the corresponding ,circle 
,,ag was illuminated1 and the ,circle bh
 with the same sort by which the        
corresponding ,circle ,,bh was          
illuminated1 and the rest of the        
,circles ci1 dk1 el1 fm respectively1   
with the same sorts of ,rays by which   
the several corresponding ,circles ,,cj1
 ,,dk1 ,,el1 ,,fm were illuminated4 ,in 
the ,figure ,,pt composed of the greater
 ,circles1 three of those ,circles ,,ag1
 ,,bh1 ,,cj1 are so expanded into one   
another1 that the three sorts of ,rays  
by which those ,circles are illuminated1
 together with other innumerable sorts  
of intermediate ,rays1 are mixed at ,,qr
 in the middle of the ,circle ,,bh4 ,and
 the like ,mixture happens throughout   

almost the whole length of the ,figure  
,,pt4 ,but in the ,figure pt composed of
 the less ,circles1 the three less      
,circles ag1 bh1 ci1 which answer to    
those three greater1 do not extend into 
one another2 nor are there any where    
mingled so much as any two of the three 
sorts of ,rays by which those ,circles  
are illuminated1 and which in the       
,figure ,,pt are all of them            
intermingled at ,,bh4  ,now he that     
shall thus consider it1 will easily     
understand that the ,mixture is         
diminished in the same ,proportion with 
the ,diameters of the ,circles4 ,if the 
,diameters of the ,circles whilst their 
,centers remain the same1 be made three 
times less than before1 the ,mixture    
will be also three times less2 if ten   
times less1 the ,mixture will be ten    
times less1 and so of other             
,proportions4 ,that is1 the ,mixture of 
the ,rays in the greater ,figure ,,pt   
will be to their ,mixture in the less   
pt1 as the ,latitude of the greater     

,figure is to the ,latitude of the less4
 ,for the ,latitudes of these ,figures  
are equal to the ,diameters of their    
,circles4 ,and hence it easily follows1 
that the ,mixture of the ,rays in the   
refracted ,spectrum pt is to the        
,mixture of the ,rays in the direct and 
immediate ,light of the ,sun1 as the    
breadth of that ,spectrum is to the     
difference between the length and       
breadth of the same ,spectrum4  ,so     
then1 if we would diminish the ,mixture 
of the ,rays1 we are to diminish the    
,diameters of the ,circles4 ,now these  
would be diminished if the ,sun's       
,diameter to which they answer could be 
made less than it is1 or 7which comes to
 the same ,purpose7 if without ,doors1  
at a great distance from the ,prism     
towards the ,sun1 some opake ,body were 
placed1 with a round hole in the middle 
of it1 to intercept all the ,sun's      
,light1 excepting so much as coming from
 the middle of his ,body could pass     
through that ,hole to the ,prism4 ,for  

so the ,circles ,,ag1 ,,bh1 and the     
rest1 would not any longer answer to the
 whole ,disque of the ,sun1 but only to 
that ,part of it which could be seen    
from the ,prism through that ,hole1 that
 it is to the apparent ,magnitude of    
that ,hole view'd from the ,prism4 ,but 
that these ,circles may answer more     
distinctly to that ,hole1 a ,lens is to 
be placed by the ,prism to cast the     
,image of the ,hole1 7that is1 every one
 of the ,circles ,,ag1 ,,bh1 c47        
distinctly upon the ,paper at ,,pt1     
after such a manner1 as by a ,lens      
placed at a ,window1 the ,species of    
,objects abroad are cast distinctly upon
 a ,paper within the ,room1 and the     
rectilinear ,sides of the oblong ,solar 
,image in the fifth ,experiment became  
distinct without any ,penumbra4 ,if this
 be done1 it will not be necessary to   
place that ,hole very far off1 no not   
beyond the ,window4 ,and therefore      
instead of that ,hole1 ,i used the ,hole
 in the ,window-shut1 as follows4       

,exper4 #aa4 ,in the ,sun's ,light let  
into my darken'd ,chamber through a     
small round ,hole in my ,window-shut1 at
 about ten or twelve ,feet from the     
,window1 ,i placed a ,lens1 by which the
 ,image of the ,hole might be distinctly
 cast upon a ,sheet of white ,paper1    
placed at the distance of six1 eight1   
ten1 or twelve ,feet from the ,lens4    
,for1 according to the difference of the
 ,lenses ,i used various distances1     
which ,i think not worth the while to   
describe4 ,then immediately after the   
,lens ,i placed a ,prism1 by which the  
trajected ,light might be refracted     
either upwards or sideways1 and thereby 
the round ,image1 which the ,lens alone 
did cast upon the ,paper might be drawn 
out into a long one with ,parallel      
,sides1 as in the third ,experiment4    
,this oblong ,image ,i let fall upon    
another ,paper at about the same        
distance from the ,prism as before1     
moving the ,paper either towards the    
,prism or from it1 until ,i found the   

just distance where the ,rectilinear    
,sides of the ,image became most        
distinct4 ,for in this ,case1 the       
,circular ,images of the ,hole1 which   
compose that ,image after the same      
manner that the ,circles ag1 bh1 ci1 c4 
do the ,figure pt in ,fig4 #bc4 were    
terminated most distinctly without any  
,penumbra1 and therefore extended into  
one another the least that they could1  
and by consequence the ,mixture of the  
heterogeneous ,rays was now the least of
 all4 ,by this means ,i used to form an 
oblong ,image 7such as is pt7 in ,fig4  
#bc1 and #bd4 of ,circular ,images of   
the ,hole1 7such as are ag1 bh1 ci1 c47 
and by using a greater or less ,hole in 
the ,window-shut1 ,i made the ,circular 
,images ag1 bh1 ci1 c4 of which it was  
formed1 to become greater or less at    
pleasure1 and thereby the ,mixture of   
the ,rays in the ,image pt to be as     
much1 or as little as ,i desired4       
,illustration3 ,,fig4 #bd4              
,illustration4 ,in the twenty-fourth    

,figure1 ,f represents the ,circular    
,hole in the ,window-shut1 ,,mn the     
,lens1 whereby the ,image or ,species of
 that ,hole is cast distinctly upon a   
,paper at ,j1 ,,abc the ,prism1 whereby 
the ,rays are at their emerging out of  
the ,lens refracted from ,j towards     
another ,paper at pt1 and the round     
,image at ,j is turned into an oblong   
,image pt falling on that other ,paper4 
,this ,image pt consists of ,circles    
placed one after another in a           
,rectilinear ,order1 as was sufficiently
 explained in the fifth ,experiment2 and
 these ,circles are equal to the ,circle
 ,j1 and consequently answer in         
magnitude to the ,hole ,f2 and therefore
 by diminishing that ,hole they may be  
at pleasure diminished1 whilst their    
,centers remain in their ,places4 ,by   
this means ,i made the ,breadth of the  
,image pt to be forty times1 and        
sometimes sixty or seventy times less   
than its ,length4 ,as for instance1 if  
the ,breadth of the ,hole ,f be one     

tenth of an ,inch1 and ,,mf the distance
 of the ,lens from the ,hole be #ab     
,feet2 and if p,b or p,m the distance of
 the ,image pt from the ,prism or ,lens 
be #aj ,feet1 and the refracting ,angle 
of the ,prism be #fb ,degrees1 the      
,breadth of the ,image pt will be one   
twelfth of an ,inch1 and the ,length    
about six ,inches1 and therefore the    
,length to the ,breadth as #gb to #a1   
and by consequence the ,light of this   
,image #ga times less compound than the 
,sun's direct ,light4 ,and ,light thus  
far simple and homogeneal1 is sufficient
 for trying all the ,experiments in this
 ,book about simple ,light4 ,for the    
,composition of heterogeneal ,rays is in
 this ,light so little1 that it is      
scarce to be discovered and perceiv'd by
 ,sense1 except perhaps in the indigo   
and violet4 ,for these being dark       
,colours do easily suffer a sensible    
,allay by that little scattering ,light 
which uses to be refracted irregularly  
by the ,inequalities of the ,prism4     

,yet instead of the ,circular ,hole ,f1 
'tis better to substitute an oblong     
,hole shaped like a long ,parallelogram 
with its ,length parallel to the ,prism 
,,abc4 ,for if this ,hole be an ,inch or
 two long1 and but a tenth or twentieth 
,part of an ,inch broad1 or narrower2   
the ,light of the ,image pt will be as  
simple as before1 or simpler1 and the   
,image will become much broader1 and    
therefore more fit to have ,experiments 
try'd in its ,light than before4        
,instead of this ,parallelogram ,hole   
may be substituted a triangular one of  
equal ,sides1 whose ,base1 for instance1
 is about the tenth ,part of an ,inch1  
and its ,height an ,inch or more4 ,for  
by this means1 if the ,axis of the      
,prism be parallel to the ,perpendicular
 of the ,triangle1 the ,image pt in     
,fig4 #be4 will now be form'd of        
equicrural ,triangles ag1 bh1 ci1 dk1   
el1 fm1 c4 and innumerable other        
intermediate ones answering to the      
triangular ,hole in ,shape and ,bigness1

 and lying one after another in a       
continual ,series between two ,parallel 
,lines af and gm4 ,these ,triangles are 
a little intermingled at their ,bases1  
but not at their ,vertices2 and         
therefore the ,light on the brighter    
,side af of the ,image1 where the ,bases
 of the ,triangles are1 is a little     
compounded1 but on the darker ,side gm  
is altogether uncompounded1 and in all  
,places between the ,sides the          
,composition is proportional to the     
distances of the ,places from that      
obscurer ,side gm4 ,and having a        
,spectrum pt of such a ,composition1 we 
may try ,experiments either in its      
stronger and less simple ,light near the
 ,side af1 or in its weaker and simpler 
,light near the other ,side gm1 as it   
shall seem most convenient4             
,illustration3 ,,fig4 #be4  ,but in     
making ,experiments of this kind1 the   
,chamber ought to be made as dark as can
 be1 lest any ,foreign ,light mingle it 
self with the ,light of the ,spectrum   

pt1 and render it compound2 especially  
if we would try ,experiments in the more
 simple ,light next the ,side gm of the 
,spectrum2 which being fainter1 will    
have a less proportion to the ,foreign  
,light2 and so by the mixture of that   
,light be more troubled1 and made more  
compound4 ,the ,lens also ought to be   
good1 such as may serve for optical     
,uses1 and the ,prism ought to have a   
large ,angle1 suppose of #fe or #gj     
,degrees1 and to be well wrought1 being 
made of ,glass free from ,bubbles and   
,veins1 with its ,sides not a little    
convex or concave1 as usually happens1  
but truly plane1 and its ,polish        
elaborate1 as in working                
,optick-glasses1 and not such as is     
usually wrought with ,putty1 whereby the
 edges of the ,sand-holes being worn    
away1 there are left all over the ,glass
 a numberless ,company of very little   
convex polite ,risings like ,waves4 ,the
 edges also of the ,prism and ,lens1 so 
far as they may make any irregular      

,refraction1 must be covered with a     
black ,paper glewed on4 ,and all the    
,light of the ,sun's ,beam let into the 
,chamber1 which is useless and          
unprofitable to the ,experiment1 ought  
to be intercepted with black ,paper1 or 
other black ,obstacles4 ,for otherwise  
the useless ,light being reflected every
 way in the ,chamber1 will mix with the 
oblong ,spectrum1 and help to disturb   
it4 ,in trying these ,things1 so much   
diligence is not altogether necessary1  
but it will promote the ,success of the 
,experiments1 and by a very scrupulous  
,examiner of ,things deserves to be     
apply'd4 ,it's difficult to get ,glass  
,prisms fit for this ,purpose1 and      
therefore ,i used sometimes prismatick  
,vessels made with pieces of broken     
,looking-glasses1 and filled with ,rain 
,water4 ,and to increase the            
,refraction1 ,i sometimes impregnated   
the ,water strongly with ,saccharum     
,saturni4   ,,prop4 ,v4 ,,theor4 ,,iv4  
,homogeneal ,light is refracted         

regularly without any ,dilatation       
splitting or shattering of the ,rays1   
and the confused ,vision of ,objects    
seen through refracting ,bodies by      
heterogeneal ,light arises from the     
different ,refrangibility of several    
sorts of ,rays4  ,the first ,part of    
this ,proposition has been already      
sufficiently proved in the fifth        
,experiment1 and will farther appear by 
the ,experiments which follow4  ,exper4 
#ab4 ,in the middle of a black ,paper ,i
 made a round ,hole about a fifth or    
sixth ,part of an ,inch in diameter4    
,upon this ,paper ,i caused the         
,spectrum of homogeneal ,light described
 in the former ,proposition1 so to fall1
 that some part of the ,light might pass
 through the ,hole of the ,paper4 ,this 
transmitted part of the ,light ,i       
refracted with a ,prism placed behind   
the ,paper1 and letting this refracted  
,light fall perpendicularly upon a white
 ,paper two or three ,feet distant from 
the ,prism1 ,i found that the ,spectrum 

formed on the ,paper by this ,light was 
not oblong1 as when 'tis made 7in the   
third ,experiment7 by refracting the    
,sun's compound ,light1 but was 7so far 
as ,i could judge by my ,eye7 perfectly 
circular1 the ,length being no greater  
than the ,breadth4 ,which shews1 that   
this ,light is refracted regularly      
without any ,dilatation of the ,rays4   
,exper4 #ac4 ,in the homogeneal ,light  
,i placed a ,paper ,circle of a quarter 
of an ,inch in diameter1 and in the     
,sun's unrefracted heterogeneal white   
,light ,i placed another ,paper ,circle 
of the same ,bigness4 ,and going from   
the ,papers to the distance of some     
,feet1 ,i viewed both ,circles through a
 ,prism4 ,the ,circle illuminated by the
 ,sun's heterogeneal ,light appeared    
very oblong1 as in the fourth           
,experiment1 the ,length being many     
times greater than the ,breadth2 but the
 other ,circle1 illuminated with        
homogeneal ,light1 appeared circular and
 distinctly defined1 as when 'tis view'd

 with the naked ,eye4 ,which proves the 
whole ,proposition4  ,exper4 #ad4 ,in   
the homogeneal ,light ,i placed ,flies1 
and such-like minute ,objects1 and      
viewing them through a ,prism1 ,i saw   
their ,parts as distinctly defined1 as  
if ,i had viewed them with the naked    
,eye4 ,the same ,objects placed in the  
,sun's unrefracted heterogeneal ,light1 
which was white1 ,i viewed also through 
a ,prism1 and saw them most confusedly  
defined1 so that ,i could not           
distinguish their smaller ,parts from   
one another4 ,i placed also the ,letters
 of a small print1 one while in the     
homogeneal ,light1 and then in the      
heterogeneal1 and viewing them through a
 ,prism1 they appeared in the latter    
,case so confused and indistinct1 that  
,i could not read them2 but in the      
former they appeared so distinct1 that  
,i could read readily1 and thought ,i   
saw them as distinct1 as when ,i view'd 
them with my naked ,eye4 ,in both ,cases
 ,i view'd the same ,objects1 through   

the same ,prism at the same distance    
from me1 and in the same ,situation4    
,there was no difference1 but in the    
,light by which the ,objects were       
illuminated1 and which in one ,case was 
simple1 and in the other compound2 and  
therefore1 the distinct ,vision in the  
former ,case1 and confused in the       
latter1 could arise from nothing else   
than from that difference of the        
,lights4 ,which proves the whole        
,proposition4  ,and in these three      
,experiments it is farther very         
remarkable1 that the ,colour of         
homogeneal ,light was never changed by  
the ,refraction4   ,,prop4 ,,vi4        
,,theor4 ,v4  ,the ,sine of ,incidence  
of every ,ray considered apart1 is to   
its ,sine of ,refraction in a given     
,ratio4  ,that every ,ray consider'd    
apart1 is constant to it self in some   
degree of ,refrangibility1 is           
sufficiently manifest out of what has   
been said4 ,those ,rays1 which in the   
first ,refraction1 are at equal         

,incidences most refracted1 are also in 
the following ,refractions at equal     
,incidences most refracted2 and so of   
the least refrangible1 and the rest     
which have any mean ,degree of          
,refrangibility1 as is manifest by the  
fifth1 sixth1 seventh1 eighth1 and ninth
 ,experiments4 ,and those which the     
first ,time at like ,incidences are     
equally refracted1 are again at like    
,incidences equally and uniformly       
refracted1 and that whether they be     
refracted before they be separated from 
one another1 as in the fifth            
,experiment1 or whether they be         
refracted apart1 as in the twelfth1     
thirteenth and fourteenth ,experiments4 
,the ,refraction therefore of every ,ray
 apart is regular1 and what ,rule that  
,refraction observes we are now to      
shew4,e  ,the late ,writers in ,opticks 
teach1 that the ,sines of ,incidence are
 in a given ,proportion to the ,sines of
 ,refraction1 as was explained in the   
fifth ,axiom1 and some by ,instruments  

fitted for measuring of ,refractions1 or
 otherwise experimentally examining this
 ,proportion1 do acquaint us that they  
have found it accurate4 ,but whilst     
they1 not understanding the different   
,refrangibility of several ,rays1       
conceived them all to be refracted      
according to one and the same           
,proportion1 'tis to be presumed that   
they adapted their ,measures only to the
 middle of the refracted ,light2 so that
 from their ,measures we may conclude   
only that the ,rays which have a mean   
,degree of ,refrangibility1 that is1    
those which when separated from the rest
 appear green1 are refracted according  
to a given ,proportion of their ,sines4 
,and therefore we are now to shew1 that 
the like given ,proportions obtain in   
all the rest4 ,that it should be so is  
very reasonable1 ,nature being ever     
conformable to her self2 but an         
experimental ,proof is desired4 ,and    
such a ,proof will be had1 if we can    
shew that the ,sines of ,refraction of  

,rays differently refrangible are one to
 another in a given ,proportion when    
their ,sines of ,incidence are equal4   
,for1 if the ,sines of ,refraction of   
all the ,rays are in given ,proportions 
to the ,sine of ,refractions of a ,ray  
which has a mean ,degree of             
,refrangibility1 and this ,sine is in a 
given ,proportion to the equal ,sines of
 ,incidence1 those other ,sines of      
,refraction will also be in given       
,proportions to the equal ,sines of     
,incidence4 ,now1 when the ,sines of    
,incidence are equal1 it will appear by 
the following ,experiment1 that the     
,sines of ,refraction are in a given    
,proportion to one another4             
,illustration3 ,,fig4 #bf4  ,exper4 #ae4
 ,the ,sun shining into a dark ,chamber 
through a little round ,hole in the     
,window-shut1 let ,s in ,fig4 #bf4      
represent his round white ,image painted
 on the opposite ,wall by his direct    
,light1 ,,pt his oblong coloured ,image 
made by refracting that ,light with a   

,prism placed at the ,window2 and pt1 or
 #bp #bt1 #cp #ct1 his oblong colour'd  
,image made by refracting again the same
 ,light sideways with a second ,prism   
placed immediately after the first in a 
cross ,position to it1 as was explained 
in the fifth ,experiment2 that is to    
say1 pt when the ,refraction of the     
second ,prism is small1 #bp #bt when its
 ,refraction is greater1 and #cp #ct    
when it is greatest4 ,for such will be  
the diversity of the ,refractions1 if   
the refracting ,angle of the second     
,prism be of various ,magnitudes2       
suppose of fifteen or twenty ,degrees to
 make the ,image pt1 of thirty or forty 
to make the ,image #bp #bt1 and of sixty
 to make the ,image #cp #ct4 ,but for   
want of solid ,glass ,prisms with       
,angles of convenient ,bignesses1 there 
may be ,vessels made of polished ,plates
 of ,glass cemented together in the form
 of ,prisms and filled with ,water4     
,these things being thus ordered1 ,i    
observed that all the solar ,images or  

coloured ,spectrums ,,pt1 pt1 #bp #bt1  
#cp #ct did very nearly converge to the 
place ,s on which the direct ,light of  
the ,sun fell and painted his white     
round ,image when the ,prisms were taken
 away4 ,the ,axis of the ,spectrum ,,pt1
 that is the ,line drawn through the    
middle of it parallel to its rectilinear
 ,sides1 did when produced pass exactly 
through the middle of that white round  
,image ,s4 ,and when the ,refraction of 
the second ,prism was equal to the      
,refraction of the first1 the refracting
 ,angles of them both being about #fj   
,degrees1 the ,axis of the ,spectrum #cp
 #ct made by that ,refraction1 did when 
produced pass also through the middle of
 the same white round ,image ,s4 ,but   
when the ,refraction of the second      
,prism was less than that of the first1 
the produced ,axes of the ,spectrums tp 
or #bt #bp made by that ,refraction did 
cut the produced ,axis of the ,spectrum 
,,tp in the points m and n1 a little    
beyond the ,center of that white round  

,image ,s4 ,whence the proportion of the
 ,line #ct,t to the ,line #cp,p was a   
little greater than the ,proportion of  
#bt,t or #bp,p1 and this ,proportion a  
little greater than that of t,t to p,p4 
,now when the ,light of the ,spectrum   
,,pt falls perpendicularly upon the     
,wall1 those ,lines #ct,t1 #cp,p1 and   
#bt,t1 and #bp,p1 and t,t1 p,p1 are the 
,tangents of the ,refractions1 and      
therefore by this ,experiment the       
,proportions of the ,tangents of the    
,refractions are obtained1 from whence  
the ,proportions of the ,sines being    
derived1 they come out equal1 so far as 
by viewing the ,spectrums1 and using    
some mathematical ,reasoning ,i could   
estimate4 ,for ,i did not make an       
accurate ,computation4 ,so then the     
,proposition holds true in every ,ray   
apart1 so far as appears by ,experiment4
 ,and that it is accurately true1 may be
 demonstrated upon this ,supposition4   
,that ,bodies refract ,light by acting  
upon its ,rays in ,lines perpendicular  

to their ,surfaces4 ,but in order to    
this ,demonstration1 ,i must distinguish
 the ,motion of every ,ray into two     
,motions1 the one perpendicular to the  
refracting ,surface1 the other parallel 
to it1 and concerning the perpendicular 
,motion lay down the following          
,proposition4  ,if any ,motion or moving
 thing whatsoever be incident with any  
,velocity on any broad and thin space   
terminated on both sides by two parallel
 ,planes1 and in its ,passage through   
that space be urged perpendicularly     
towards the farther ,plane by any force 
which at given distances from the ,plane
 is of given ,quantities2 the           
perpendicular velocity of that ,motion  
or ,thing1 at its emerging out of that  
space1 shall be always equal to the     
square ,root of the sum of the square of
 the perpendicular velocity of that     
,motion or ,thing at its ,incidence on  
that space2 and of the square of the    
perpendicular velocity which that       
,motion or ,thing would have at its     

,emergence1 if at its ,incidence its    
perpendicular velocity was infinitely   
little4  ,and the same ,proposition     
holds true of any ,motion or ,thing     
perpendicularly retarded in its passage 
through that space1 if instead of the   
sum of the two ,squares you take their  
difference4 ,the ,demonstration         
,mathematicians will easily find out1   
and therefore ,i shall not trouble the  
,reader with it4  ,suppose now that a   
,ray coming most obliquely in the ,line 
,,mc in ,fig4 #a4 be refracted at ,c by 
the ,plane ,,rs into the ,line ,,cn1 and
 if it be required to find the ,line    
,,ce1 into which any other ,ray ,,ac    
shall be refracted2 let ,,mc1 ,,ad1 be  
the ,sines of ,incidence of the two     
,rays1 and ,,ng1 ,,ef1 their ,sines of  
,refraction1 and let the equal ,motions 
of the incident ,rays be represented by 
the equal ,lines ,,mc and ,,ac1 and the 
,motion ,,mc being considered as        
parallel to the refracting ,plane1 let  
the other ,motion ,,ac be distinguished 

into two ,motions ,,ad and ,,dc1 one of 
which ,,ad is parallel1 and the other   
,,dc perpendicular to the refracting    
,surface4 ,in like manner1 let the      
,motions of the emerging ,rays be       
distinguish'd into two1 whereof the     
perpendicular ones are ,,mc_/,,ng x ,,cg
 and ,,ad_/,,ef x ,,cf4 ,and if the     
force of the refracting ,plane begins to
 act upon the ,rays either in that      
,plane or at a certain distance from it 
on the one side1 and ends at a certain  
distance from it on the other side1 and 
in all places between those two limits  
acts upon the ,rays in ,lines           
perpendicular to that refracting ,plane1
 and the ,actions upon the ,rays at     
equal distances from the refracting     
,plane be equal1 and at unequal ones    
either equal or unequal according to any
 rate whatever2 that ,motion of the ,ray
 which is parallel to the refracting    
,plane1 will suffer no ,alteration by   
that ,force2 and that ,motion which is  
perpendicular to it will be altered     

according to the rule of the foregoing  
,proposition4 ,if therefore for the     
perpendicular velocity of the emerging  
,ray ,,cn you write ,,mc_/,,ng x ,,cg as
 above1 then the perpendicular velocity 
of any other emerging ,ray ,,ce which   
was ,,ad_/,,ef x ,,cf1 will be equal to 
the square ,root of ,,cdq  7,m,cq_/,n,gq
 x ,,cgq74 ,and by squaring these       
,equals1 and adding to them the ,equals 
,,adq and ,,mcq - ,,cdq1 and dividing   
the ,sums by the ,equals ,,cfq  ,,efq   
and ,,cgq  ,,ngq1 you will have         
,m,cq_/,n,gq equal to ,a,dq_/,e,fq4     
,whence ,,ad1 the ,sine of ,incidence1  
is to ,,ef the ,sine of ,refraction1 as 
,,mc to ,,ng1 that is1 in a given ratio4
 ,and this ,demonstration being general1
 without determining what ,light is1 or 
by what kind of ,force it is refracted1 
or assuming any thing farther than that 
the refracting ,body acts upon the ,rays
 in ,lines perpendicular to its         
,surface2 ,i take it to be a very       
convincing ,argument of the full truth  

of this ,proposition4  ,so then1 if the 
ratio of the ,sines of ,incidence and   
,refraction of any sort of ,rays be     
found in any one case1 'tis given in all
 cases2 and this may be readily found by
 the ,method in the following           
,proposition4   ,,prop4 ,,vii4 ,,theor4 
,,vi4  ,the ,perfection of ,telescopes  
is impeded by the different             
,refrangibility of the ,rays of ,light4 
,the ,imperfection of ,telescopes is    
vulgarly attributed to the spherical    
,figures of the ,glasses1 and therefore 
,mathematicians have propounded to      
figure them by the conical ,sections4   
,to shew that they are mistaken1 ,i have
 inserted this ,proposition2 the truth  
of which will appear by the measure of  
the ,refractions of the several sorts of
 ,rays2 and these measures ,i thus      
determine4  ,in the third ,experiment of
 this first ,part1 where the refracting 
,angle of the ,prism was #fb-a_/b       
,degrees1 the half of that ,angle #ca   
deg4 #ae min4 is the ,angle of          

,incidence of the ,rays at their going  
out of the ,glass into the ,air,f2 and  
the ,sine of this ,angle is #eahh1 the  
,radius being #ajjjj4 ,when the ,axis of
 this ,prism was parallel to the        
,horizon1 and the ,refraction of the    
,rays at their ,incidence on this ,prism
 equal to that at their ,emergence out  
of it1 ,i observed with a ,quadrant the 
,angle which the mean refrangible ,rays1
 7that is those which went to the middle
 of the ,sun's coloured ,image7 made    
with the ,horizon1 and by this ,angle   
and the ,sun's altitude observed at the 
same time1 ,i found the ,angle which the
 emergent ,rays contained with the      
incident to be #dd deg4 and #dj min4 and
 the half of this ,angle added to the   
,angle of ,incidence #ca deg4 #ae min4  
makes the ,angle of ,refraction1 which  
is therefore #ec deg4 #ce min4 and its  
,sine #hjdg4 ,these are the ,sines of   
,incidence and ,refraction of the mean  
refrangible ,rays1 and their ,proportion
 in round ,numbers is #bj to #ca4 ,this 

,glass was of a ,colour inclining to    
green4 ,the last of the ,prisms         
mentioned in the third ,experiment was  
of clear white ,glass4 ,its refracting  
,angle #fc-a_/b ,degrees4 ,the ,angle   
which the emergent ,rays contained1 with
 the incident #de deg4 #ej min4 ,the    
,sine of half the first ,angle #ebfb4   
,the ,sine of half the ,sum of the      
,angles #haeg4 ,and their ,proportion in
 round ,numbers #bj to #ca1 as before4  
,from the ,length of the ,image1 which  
was about #i-c_/d or #aj ,inches1       
subduct its ,breadth1 which was #b-a_/h 
,inches1 and the ,remainder #g-c_/d     
,inches would be the ,length of the     
,image were the ,sun but a ,point1 and  
therefore subtends the ,angle which the 
most and least refrangible ,rays1 when  
incident on the ,prism in the same      
,lines1 do contain with one another     
after their ,emergence4 ,whence this    
,angle is #b deg4 #j'4 #g''4 ,for the   
distance between the ,image and the     
,prism where this ,angle is made1 was   

#ah-a_/b ,feet1 and at that distance the
 ,chord #g-c_/d ,inches subtends an     
,angle of #b deg4 #j'4 #g''4 ,now half  
this ,angle is the ,angle which these   
emergent ,rays contain with the emergent
 mean refrangible ,rays1 and a quarter  
thereof1 that is #cj'4 #b''4 may be     
accounted the ,angle which they would   
contain with the same emergent mean     
refrangible ,rays1 were they co-incident
 to them within the ,glass1 and suffered
 no other ,refraction than that at their
 ,emergence4 ,for1 if two equal         
,refractions1 the one at the ,incidence 
of the ,rays on the ,prism1 the other at
 their ,emergence1 make half the ,angle 
#b deg4 #j'4 #g''4 then one of those    
,refractions will make about a quarter  
of that ,angle1 and this quarter added  
to1 and subducted from the ,angle of    
,refraction of the mean refrangible     
,rays1 which was #ec deg4 #ce'1 gives   
the ,angles of ,refraction of the most  
and least refrangible ,rays #ed deg4 #e'
 #b''1 and #ec deg4 #d' #eh''1 whose    

,sines are #hjii and #giie1 the common  
,angle of ,incidence being #ca deg4     
#ae'1 and its ,sine #eahh2 and these    
,sines in the least round ,numbers are  
in proportion to one another1 as #gh and
 #gg to #ej4  ,now1 if you subduct the  
common ,sine of ,incidence #ej from the 
,sines of ,refraction #gg and #gh1 the  
,remainders #bg and #bh shew1 that in   
small ,refractions the ,refraction of   
the least refrangible ,rays is to the   
,refraction of the most refrangible     
ones1 as #bg to #bh very nearly1 and    
that the difference of the ,refractions 
of the least refrangible and most       
refrangible ,rays is about the          
#bg-a_/bth ,part of the whole           
,refraction of the mean refrangible     
,rays4  ,whence they that are skilled in
 ,opticks will easily understand1,g that
 the ,breadth of the least circular     
,space1 into which ,object-glasses of   
,telescopes can collect all sorts of    
,parallel ,rays1 is about the #bg-a_/bth
 ,part of half the ,aperture of the     

,glass1 or #eeth ,part of the whole     
,aperture2 and that the ,focus of the   
most refrangible ,rays is nearer to the 
,object-glass than the ,focus of the    
least refrangible ones1 by about the    
#bg-a_/bth ,part of the distance between
 the ,object-glass and the ,focus of the
 mean refrangible ones4  ,and if ,rays  
of all sorts1 flowing from any one lucid
 ,point in the ,axis of any convex      
,lens1 be made by the ,refraction of the
 ,lens to converge to ,points not too   
remote from the ,lens1 the ,focus of the
 most refrangible ,rays shall be nearer 
to the ,lens than the ,focus of the     
least refrangible ones1 by a distance   
which is to the #bg-a_/bth ,part of the 
distance of the ,focus of the mean      
refrangible ,rays from the ,lens1 as the
 distance between that ,focus and the   
lucid ,point1 from whence the ,rays     
flow1 is to the distance between that   
lucid ,point and the ,lens very nearly4 
,now to examine whether the ,difference 
between the ,refractions1 which the most

 refrangible and the least refrangible  
,rays flowing from the same ,point      
suffer in the ,object-glasses of        
,telescopes and such-like ,glasses1 be  
so great as is here described1 ,i       
contrived the following ,experiment4    
,exper4 #af4 ,the ,lens which ,i used in
 the second and eighth ,experiments1    
being placed six ,feet and an ,inch     
distant from any ,object1 collected the 
,species of that ,object by the mean    
refrangible ,rays at the distance of six
 ,feet and an ,inch from the ,lens on   
the other side4 ,and therefore by the   
foregoing ,rule1 it ought to collect the
 ,species of that ,object by the least  
refrangible ,rays at the distance of six
 ,feet and #c-b_/c ,inches from the     
,lens1 and by the most refrangible ones 
at the distance of five ,feet and       
#aj-a_/c ,inches from it3 ,so that      
between the two ,places1 where these    
least and most refrangible ,rays collect
 the ,species1 there may be the distance
 of about #e-a_/c ,inches4 ,for by that 

,rule1 as six ,feet and an ,inch 7the   
distance of the ,lens from the lucid    
,object7 is to twelve ,feet and two     
,inches 7the distance of the lucid      
,object from the ,focus of the mean     
refrangible ,rays7 that is1 as ,one is  
to ,two2 so is the #bg-a_/bth ,part of  
six ,feet and an ,inch 7the distance    
between the ,lens and the same ,focus7  
to the distance between the ,focus of   
the most refrangible ,rays and the      
,focus of the least refrangible ones1   
which is therefore #e-ag_/ee ,inches1   
that is very nearly #e-a_/c ,inches4    
,now to know whether this ,measure was  
true1 ,i repeated the second and eighth 
,experiment with coloured ,light1 which 
was less compounded than that ,i there  
made use of3 ,for ,i now separated the  
heterogeneous ,rays from one another by 
the ,method ,i described in the eleventh
 ,experiment1 so as to make a coloured  
,spectrum about twelve or fifteen ,times
 longer than broad4 ,this ,spectrum ,i  
cast on a printed ,book1 and placing the

 above-mentioned ,lens at the distance  
of six ,feet and an ,inch from this     
,spectrum to collect the ,species of the
 illuminated ,letters at the same       
distance on the other side1 ,i found    
that the ,species of the ,letters       
illuminated with blue were nearer to the
 ,lens than those illuminated with deep 
red by about three ,inches1 or three and
 a quarter2 but the ,species of the     
,letters illuminated with indigo and    
violet appeared so confused and         
indistinct1 that ,i could not read them3
 ,whereupon viewing the ,prism1 ,i found
 it was full of ,veins running from one 
end of the ,glass to the other2 so that 
the ,refraction could not be regular4 ,i
 took another ,prism therefore which was
 free from ,veins1 and instead of the   
,letters ,i used two or three ,parallel 
black ,lines a little broader than the  
,strokes of the ,letters1 and casting   
the ,colours upon these ,lines in such  
manner1 that the ,lines ran along the   
,colours from one end of the ,spectrum  

to the other1 ,i found that the ,focus  
where the indigo1 or confine of this    
,colour and violet cast the ,species of 
the black ,lines most distinctly1 to be 
about four ,inches1 or #d-a_/d nearer to
 the ,lens than the ,focus1 where the   
deepest red cast the ,species of the    
same black ,lines most distinctly4 ,the 
violet was so faint and dark1 that ,i   
could not discern the ,species of the   
,lines distinctly by that ,colour2 and  
therefore considering that the ,prism   
was made of a dark coloured ,glass      
inclining to green1 ,i took another     
,prism of clear white ,glass2 but the   
,spectrum of ,colours which this ,prism 
made had long white ,streams of faint   
,light shooting out from both ends of   
the ,colours1 which made me conclude    
that something was amiss2 and viewing   
the ,prism1 ,i found two or three little
 ,bubbles in the ,glass1 which refracted
 the ,light irregularly4 ,wherefore ,i  
covered that ,part of the ,glass with   
black ,paper1 and letting the ,light    

pass through another ,part of it which  
was free from such ,bubbles1 the        
,spectrum of ,colours became free from  
those irregular ,streams of ,light1 and 
was now such as ,i desired4 ,but still  
,i found the violet so dark and faint1  
that ,i could scarce see the ,species of
 the ,lines by the violet1 and not at   
all by the deepest ,part of it1 which   
was next the end of the ,spectrum4 ,i   
suspected therefore1 that this faint and
 dark ,colour might be allayed by that  
scattering ,light which was refracted1  
and reflected irregularly1 partly by    
some very small ,bubbles in the         
,glasses1 and partly by the             
,inequalities of their ,polish2 which   
,light1 tho' it was but little1 yet it  
being of a white ,colour1 might suffice 
to affect the ,sense so strongly as to  
disturb the ,phaenomena of that weak and
 dark ,colour the violet1 and therefore 
,i tried1 as in the #abth1 #acth1 and   
#adth ,experiments1 whether the ,light  
of this ,colour did not consist of a    

sensible ,mixture of heterogeneous      
,rays1 but found it did not4 ,nor did   
the ,refractions cause any other        
sensible ,colour than violet to emerge  
out of this ,light1 as they would have  
done out of white ,light1 and by        
consequence out of this violet ,light   
had it been sensibly compounded with    
white ,light4 ,and therefore ,i         
concluded1 that the reason why ,i could 
not see the ,species of the ,lines      
distinctly by this ,colour1 was only the
 ,darkness of this ,colour1 and         
,thinness of its ,light1 and its        
distance from the ,axis of the ,lens2 ,i
 divided therefore those ,parallel black
 ,lines into equal ,parts1 by which ,i  
might readily know the distances of the 
,colours in the ,spectrum from one      
another1 and noted the distances of the 
,lens from the ,foci of such ,colours1  
as cast the ,species of the ,lines      
distinctly1 and then considered whether 
the difference of those distances bear  
such proportion to #e-a_/c ,inches1 the 

greatest ,difference of the distances1  
which the ,foci of the deepest red and  
violet ought to have from the ,lens1 as 
the distance of the observed ,colours   
from one another in the ,spectrum bear  
to the greatest distance of the deepest 
red and violet measured in the          
,rectilinear ,sides of the ,spectrum1   
that is1 to the ,length of those ,sides1
 or ,excess of the ,length of the       
,spectrum above its ,breadth4 ,and my   
,observations were as follows4  ,when ,i
 observed and compared the deepest      
sensible red1 and the ,colour in the    
,confine of green and blue1 which at the
 ,rectilinear ,sides of the ,spectrum   
was distant from it half the ,length of 
those ,sides1 the ,focus where the      
,confine of green and blue cast the     
,species of the ,lines distinctly on the
 ,paper1 was nearer to the ,lens than   
the ,focus1 where the red cast those    
,lines distinctly on it by about #b-a_/b
 or #b-c_/d ,inches4 ,for sometimes the 
,measures were a little greater1        

sometimes a little less1 but seldom     
varied from one another above #a_/c of  
an ,inch4 ,for it was very difficult to 
define the ,places of the ,foci1 without
 some little ,errors4 ,now1 if the      
,colours distant half the ,length of the
 ,image1 7measured at its ,rectilinear  
,sides7 give #b-a_/b or #b-c_/d         
,difference of the distances of their   
,foci from the ,lens1 then the ,colours 
distant the whole ,length ought to give 
#e or #e-a_/b ,inches difference of     
those distances4  ,but here it's to be  
noted1 that ,i could not see the red to 
the full end of the ,spectrum1 but only 
to the ,center of the ,semicircle which 
bounded that end1 or a little farther2  
and therefore ,i compared this red not  
with that ,colour which was exactly in  
the middle of the ,spectrum1 or ,confine
 of green and blue1 but with that which 
verged a little more to the blue than to
 the green3 ,and as ,i reckoned the     
whole ,length of the ,colours not to be 
the whole ,length of the ,spectrum1 but 

the ,length of its ,rectilinear ,sides1 
so compleating the semicircular ,ends   
into ,circles1 when either of the       
observed ,colours fell within those     
,circles1 ,i measured the distance of   
that ,colour from the semicircular ,end 
of the ,spectrum1 and subducting half   
this distance from the measured distance
 of the two ,colours1 ,i took the       
,remainder for their corrected distance2
 and in these ,observations set down    
this corrected distance for the         
difference of the distances of their    
,foci from the ,lens4 ,for1 as the      
,length of the ,rectilinear ,sides of   
the ,spectrum would be the whole ,length
 of all the ,colours1 were the ,circles 
of which 7as we shewed7 that ,spectrum  
consists contracted and reduced to      
,physical ,points1 so in that ,case this
 corrected distance would be the real   
distance of the two observed ,colours4  
,when therefore ,i farther observed the 
deepest sensible red1 and that blue     
whose corrected distance from it was    

#g_/ab ,parts of the ,length of the     
,rectilinear ,sides of the ,spectrum1   
the difference of the distances of their
 ,foci from the ,lens was about #c-a_/d 
,inches1 and as #g to #ab1 so is #c-a_/d
 to #e-d_/g4  ,when ,i observed the     
deepest sensible red1 and that indigo   
whose corrected distance was #h_/ab or  
#b_/c of the ,length of the ,rectilinear
 ,sides of the ,spectrum1 the difference
 of the distances of their ,foci from   
the ,lens1 was about #c-b_/c ,inches1   
and as #b to #c1 so is #c-b_/c to       
#e-a_/b4  ,when ,i observed the deepest 
sensible red1 and that deep indigo whose
 corrected distance from one another was
 #i_/ab or #c_/d of the ,length of the  
,rectilinear ,sides of the ,spectrum1   
the difference of the distances of their
 ,foci from the ,lens was about #d      
,inches2 and as #c to #d1 so is #d to   
#e-a_/c4  ,when ,i observed the deepest 
sensible red1 and that ,part of the     
violet next the indigo1 whose corrected 
distance from the red was #aj_/ab or    

#e_/f of the ,length of the ,rectilinear
 ,sides of the ,spectrum1 the difference
 of the distances of their ,foci from   
the ,lens was about #d-a_/b ,inches1 and
 as #e to #f1 so is #d-a_/b to #e-b_/e4 
,for sometimes1 when the ,lens was      
advantageously placed1 so that its ,axis
 respected the blue1 and all ,things    
else were well ordered1 and the ,sun    
shone clear1 and ,i held my ,eye very   
near to the ,paper on which the ,lens   
cast the ,species of the ,lines1 ,i     
could see pretty distinctly the ,species
 of those ,lines by that ,part of the   
violet which was next the indigo2 and   
sometimes ,i could see them by above    
half the violet1 ,for in making these   
,experiments ,i had observed1 that the  
,species of those ,colours only appear  
distinct1 which were in or near the     
,axis of the ,lens3 ,so that if the blue
 or indigo were in the ,axis1 ,i could  
see their ,species distinctly2 and then 
the red appeared much less distinct than
 before4 ,wherefore ,i contrived to make

 the ,spectrum of ,colours shorter than 
before1 so that both its ,ends might be 
nearer to the ,axis of the ,lens4 ,and  
now its ,length was about #b-a_/b       
,inches1 and ,breadth about #a_/e or    
#a_/f of an ,inch4 ,also instead of the 
black ,lines on which the ,spectrum was 
cast1 ,i made one black ,line broader   
than those1 that ,i might see its       
,species more easily2 and this ,line ,i 
divided by short cross ,lines into equal
 ,parts1 for measuring the distances of 
the observed ,colours4 ,and now ,i could
 sometimes see the ,species of this     
,line with its ,divisions almost as far 
as the ,center of the semicircular      
violet ,end of the ,spectrum1 and made  
these farther ,observations4  ,when ,i  
observed the deepest sensible red1 and  
that ,part of the violet1 whose         
corrected distance from it was about    
#h_/i ,parts of the ,rectilinear ,sides 
of the ,spectrum1 the ,difference of the
 distances of the ,foci of those        
,colours from the ,lens1 was one time   

#d-b_/c1 another time #d-c_/d1 another  
time #d-g_/h ,inches2 and as #h to #i1  
so are #d-b_/c1 #d-c_/d1 #d-g_/h1 to    
#e-a_/d1 #e-aa_/cb1 #e-ca_/fd           
respectively4  ,when ,i observed the    
deepest sensible red1 and deepest       
sensible violet1 7the corrected distance
 of which ,colours1 when all ,things    
were ordered to the best ,advantage1 and
 the ,sun shone very clear1 was about   
#aa_/ab or #ae_/af ,parts of the ,length
 of the ,rectilinear ,sides of the      
coloured ,spectrum7 ,i found the        
,difference of the distances of their   
,foci from the ,lens sometimes #d-c_/d  
sometimes #e-a_/d1 and for the most part
 #e ,inches or thereabouts2 and as #aa  
to #ab1 or #ae to #af1 so is five       
,inches to #e-b_/b or #e-a_/c ,inches4  
,and by this ,progression of            
,experiments ,i satisfied my self1 that 
had the ,light at the very ,ends of the 
,spectrum been strong enough to make the
 ,species of the black ,lines appear    
plainly on the ,paper1 the ,focus of the

 deepest violet would have been found   
nearer to the ,lens1 than the ,focus of 
the deepest red1 by about #e-a_/c       
,inches at least4 ,and this is a farther
 ,evidence1 that the ,sines of          
,incidence and ,refraction of the       
several sorts of ,rays1 hold the same   
,proportion to one another in the       
smallest ,refractions which they do in  
the greatest4  ,my ,progress in making  
this nice and troublesome ,experiment ,i
 have set down more at large1 that they 
that shall try it after me may be aware 
of the ,circumspection requisite to make
 it succeed well4 ,and if they cannot   
make it succeed so well as ,i did1 they 
may notwithstanding collect by the      
,proportion of the distance of the      
,colours of the ,spectrum1 to the       
,difference of the distances of their   
,foci from the ,lens1 what would be the 
,success in the more distant ,colours by
 a better trial4 ,and yet1 if they use a
 broader ,lens than ,i did1 and fix it  
to a long strait ,staff1 by means of    

which it may be readily and truly       
directed to the ,colour whose ,focus is 
desired1 ,i question not but the        
,experiment will succeed better with    
them than it did with me4 ,for ,i       
directed the ,axis as nearly as ,i could
 to the middle of the ,colours1 and then
 the faint ,ends of the ,spectrum being 
remote from the ,axis1 cast their       
,species less distinctly on the ,paper  
than they would have done1 had the ,axis
 been successively directed to them4    
,now by what has been said1 it's certain
 that the ,rays which differ in         
,refrangibility do not converge to the  
same ,focus2 but if they flow from a    
lucid ,point1 as far from the ,lens on  
one side as their ,foci are on the      
other1 the ,focus of the most           
refrangible ,rays shall be nearer to the
 ,lens than that of the least           
refrangible1 by above the fourteenth    
,part of the whole distance2 and if they
 flow from a lucid ,point1 so very      
remote from the ,lens1 that before their

 ,incidence they may be accounted       
parallel1 the ,focus of the most        
refrangible ,rays shall be nearer to the
 ,lens than the ,focus of the least     
refrangible1 by about the #bgth or #bhth
 ,part of their whole distance from it4 
,and the ,diameter of the ,circle in the
 middle ,space between those two ,foci  
which they illuminate1 when they fall   
there on any ,plane1 perpendicular to   
the ,axis 7which ,circle is the least   
into which they can all be gathered7 is 
about the #eeth ,part of the ,diameter  
of the ,aperture of the ,glass4 ,so that
 'tis a wonder1 that ,telescopes        
represent ,objects so distinct as they  
do4 ,but were all the ,rays of ,light   
equally refrangible1 the ,error arising 
only from the ,sphericalness of the     
,figures of ,glasses would be many      
hundred times less4 ,for1 if the        
,object-glass of a ,telescope be        
,plano-convex1 and the ,plane side be   
turned towards the ,object1 and the     
,diameter of the ,sphere1 whereof this  

,glass is a ,segment1 be called ,d1 and 
the ,semi-diameter of the ,aperture of  
the ,glass be called ,s1 and the ,sine  
of ,incidence out of ,glass into ,air1  
be to the ,sine of ,refraction as ,i to 
,r2 the ,rays which come parallel to the
 ,axis of the ,glass1 shall in the      
,place where the ,image of the ,object  
is most distinctly made1 be scattered   
all over a little ,circle1 whose        
,diameter is 7,rq_/,iq7 x 7,s cub4_/,d  
quad47 very nearly1,h as ,i gather by   
computing the ,errors of the ,rays by   
the ,method of infinite ,series1 and    
rejecting the ,terms1 whose ,quantities 
are inconsiderable4 ,as for instance1 if
 the ,sine of ,incidence ,i1 be to the  
,sine of ,refraction ,r1 as #bj to #ca1 
and if ,d the ,diameter of the ,sphere1 
to which the ,convex-side of the ,glass 
is ground1 be #ajj ,feet or #abjj       
,inches1 and ,s the ,semi-diameter of   
the ,aperture be two ,inches1 the       
,diameter of the little ,circle1 7that  
is 7,rq x ,s cub47_/7,iq x ,d quad477   

will be 7#ca x #ca x #h7_/7bj x #bj x   
#abjj x #abjj7 7or #ifa_/gbjjjjjj7      
,parts of an ,inch4 ,but the ,diameter  
of the little ,circle1 through which    
these ,rays are scattered by unequal    
,refrangibility1 will be about the #eeth
 ,part of the ,aperture of the          
,object-glass1 which here is four       
,inches4 ,and therefore1 the ,error     
arising from the ,spherical ,figure of  
the ,glass1 is to the ,error arising    
from the different ,refrangibility of   
the ,rays1 as #ifa_/gbjjjjjj to #d_/ee1 
that is as #a to #eddi2 and therefore   
being in comparison so very little1     
deserves not to be considered4          
,illustration3 ,,fig4 #bg4  ,but you    
will say1 if the ,errors caused by the  
different ,refrangibility be so very    
great1 how comes it to pass1 that       
,objects appear through ,telescopes so  
distinct as they do8 ,i answer1 'tis    
because the erring ,rays are not        
scattered uniformly over all that       
,circular ,space1 but collected         

infinitely more densely in the ,center  
than in any other ,part of the ,circle1 
and in the ,way from the ,center to the 
,circumference1 grow continually rarer  
and rarer1 so as at the ,circumference  
to become infinitely rare2 and by reason
 of their ,rarity are not strong enough 
to be visible1 unless in the ,center and
 very near it4 ,let ,,ade in ,fig4 #bg4 
represent one of those ,circles         
described with the ,center ,c1 and      
,semi-diameter ,,ac1 and let ,,bfg be a 
smaller ,circle concentrick to the      
former1 cutting with its ,circumference 
the ,diameter ,,ac in ,b1 and bisect    
,,ac in ,n2 and by my reckoning1 the    
,density of the ,light in any ,place ,b1
 will be to its ,density in ,n1 as ,,ab 
to ,,bc2 and the whole ,light within the
 lesser ,circle ,,bfg1 will be to the   
whole ,light within the greater ,,aed1  
as the ,excess of the ,square of ,,ac   
above the ,square of ,,ab1 is to the    
,square of ,,ac4 ,as if ,,bc be the     
fifth ,part of ,,ac1 the ,light will be 

four times denser in ,b than in ,n1 and 
the whole ,light within the less        
,circle1 will be to the whole ,light    
within the greater1 as nine to          
twenty-five4 ,whence it's evident1 that 
the ,light within the less ,circle1 must
 strike the ,sense much more strongly1  
than that faint and dilated ,light round
 about between it and the ,circumference
 of the greater4  ,but it's farther to  
be noted1 that the most luminous of the 
,prismatick ,colours are the yellow and 
orange4 ,these affect the ,senses more  
strongly than all the rest together1 and
 next to these in strength are the red  
and green4 ,the blue compared with these
 is a faint and dark ,colour1 and the   
indigo and violet are much darker and   
fainter1 so that these compared with the
 stronger ,colours are little to be     
regarded4 ,the ,images of ,objects are  
therefore to be placed1 not in the      
,focus of the mean refrangible ,rays1   
which are in the ,confine of green and  
blue1 but in the ,focus of those ,rays  

which are in the middle of the orange   
and yellow2 there where the ,colour is  
most luminous and fulgent1 that is in   
the brightest yellow1 that yellow which 
inclines more to orange than to green4  
,and by the ,refraction of these ,rays  
7whose ,sines of ,incidence and         
,refraction in ,glass are as #ag and    
#aa7 the ,refraction of ,glass and      
,crystal for ,optical ,uses is to be    
measured4 ,let us therefore place the   
,image of the ,object in the ,focus of  
these ,rays1 and all the yellow and     
orange will fall within a ,circle1 whose
 ,diameter is about the #bejth ,part of 
the ,diameter of the ,aperture of the   
,glass4 ,and if you add the brighter    
half of the red1 7that half which is    
next the orange7 and the brighter half  
of the green1 7that half which is next  
the yellow7 about three fifth ,parts of 
the ,light of these two ,colours will   
fall within the same ,circle1 and two   
fifth ,parts will fall without it round 
about2 and that which falls without will

 be spread through almost as much more  
space as that which falls within1 and so
 in the gross be almost three times     
rarer4 ,of the other half of the red and
 green1 7that is of the deep dark red   
and willow green7 about one quarter will
 fall within this ,circle1 and three    
quarters without1 and that which falls  
without will be spread through about    
four or five times more space than that 
which falls within2 and so in the gross 
be rarer1 and if compared with the whole
 ,light within it1 will be about #be    
times rarer than all that taken in the  
gross2 or rather more than #cj or #dj   
times rarer1 because the deep red in the
 end of the ,spectrum of ,colours made  
by a ,prism is very thin and rare1 and  
the willow green is something rarer than
 the orange and yellow4 ,the ,light of  
these ,colours therefore being so very  
much rarer than that within the ,circle1
 will scarce affect the ,sense1         
especially since the deep red and willow
 green of this ,light1 are much darker  

,colours than the rest4 ,and for the    
same reason the blue and violet being   
much darker ,colours than these1 and    
much more rarified1 may be neglected4   
,for the dense and bright ,light of the 
,circle1 will obscure the rare and weak 
,light of these dark ,colours round     
about it1 and render them almost        
insensible4 ,the sensible ,image of a   
lucid ,point is therefore scarce broader
 than a ,circle1 whose ,diameter is the 
#bejth ,part of the ,diameter of the    
,aperture of the ,object-glass of a good
 ,telescope1 or not much broader1 if you
 except a faint and dark misty ,light   
round about it1 which a ,spectator will 
scarce regard4 ,and therefore in a      
,telescope1 whose ,aperture is four     
,inches1 and ,length an hundred ,feet1  
it exceeds not #b'' #de'''1 or #c''4    
,and in a ,telescope whose ,aperture is 
two ,inches1 and ,length #bj or #cj     
,feet1 it may be #e'' or #f''1 and      
scarce above4 ,and this answers well to 
,experience3 ,for some ,astronomers have

 found the ,diameters of the fix'd      
,stars1 in ,telescopes of between #bj   
and #fj ,feet in length1 to be about    
#e'' or #f''1 or at most #h'' or #aj''  
in diameter4 ,but if the ,eye-,glass be 
tincted faintly with the ,smoak of a    
,lamp or ,torch1 to obscure the ,light  
of the ,star1 the fainter ,light in the 
,circumference of the ,star ceases to be
 visible1 and the ,star 7if the ,glass  
be sufficiently soiled with ,smoak7     
appears something more like a           
mathematical ,point4 ,and for the same  
,reason1 the enormous ,part of the      
,light in the ,circumference of every   
lucid ,point ought to be less           
discernible in shorter ,telescopes than 
in longer1 because the shorter transmit 
less ,light to the ,eye4  ,now1 that the
 fix'd ,stars1 by reason of their       
immense ,distance1 appear like ,points1 
unless so far as their ,light is dilated
 by ,refraction1 may appear from hence2 
that when the ,moon passes over them and
 eclipses them1 their ,light vanishes1  

not gradually like that of the ,planets1
 but all at once2 and in the end of the 
,eclipse it returns into ,sight all at  
once1 or certainly in less time than the
 second of a ,minute2 the ,refraction of
 the ,moon's ,atmosphere a little       
protracting the time in which the ,light
 of the ,star first vanishes1 and       
afterwards returns into ,sight4  ,now1  
if we suppose the sensible ,image of a  
lucid ,point1 to be even #bej times     
narrower than the ,aperture of the      
,glass2 yet this ,image would be still  
much greater than if it were only from  
the spherical ,figure of the ,glass4    
,for were it not for the different      
,refrangibility of the ,rays1 its       
breadth in an #ajj ,foot ,telescope     
whose aperture is #d ,inches1 would be  
but #ifa_/gbjjjjjj parts of an ,inch1 as
 is manifest by the foregoing           
,computation4 ,and therefore in this    
case the greatest ,errors arising from  
the spherical ,figure of the ,glass1    
would be to the greatest sensible       

,errors arising from the different      
,refrangibility of the ,rays as         
#ifa_/gbjjjjjj to #d_/bej at most1 that 
is only as #a to #abjj4 ,and this       
sufficiently shews that it is not the   
spherical ,figures of ,glasses1 but the 
different ,refrangibility of the ,rays  
which hinders the perfection of         
,telescopes4  ,there is another         
,argument by which it may appear that   
the different ,refrangibility of ,rays1 
is the true cause of the imperfection of
 ,telescopes4 ,for the ,errors of the   
,rays arising from the spherical        
,figures of ,object-glasses1 are as the 
,cubes of the ,apertures of the ,object 
,glasses2 and thence to make ,telescopes
 of various ,lengths magnify with equal 
distinctness1 the ,apertures of the     
,object-glasses1 and the ,charges or    
magnifying ,powers ought to be as the   
,cubes of the square ,roots of their    
lengths2 which doth not answer to       
,experience4 ,but the ,errors of the    
,rays arising from the different        

,refrangibility1 are as the ,apertures  
of the ,object-glasses2 and thence to   
make ,telescopes of various lengths1    
magnify with equal distinctness1 their  
,apertures and ,charges ought to be as  
the square ,roots of their lengths2 and 
this answers to ,experience1 as is well 
known4 ,for ,instance1 a ,telescope of  
#fd ,feet in length1 with an ,aperture  
of #b-b_/c ,inches1 magnifies about #abj
 times1 with as much distinctness as one
 of a ,foot in length1 with #a_/c of an 
,inch aperture1 magnifies #ae times4    
,illustration3 ,,fig4 #bh4  ,now were it
 not for this different ,refrangibility 
of ,rays1 ,telescopes might be brought  
to a greater perfection than we have yet
 describ'd1 by composing the            
,object-glass of two ,glasses with      
,water between them4 ,let ,,adfc in     
,fig4 #bh4 represent the ,object-glass  
composed of two ,glasses ,,abed and     
,,befc1 alike convex on the outsides    
,,agd and ,,chf1 and alike concave on   
the insides ,,bme1 ,,bne1 with ,water in

 the concavity ,,bmen4 ,let the ,sine of
 ,incidence out of ,glass into ,air be  
as ,i to ,r1 and out of ,water into     
,air1 as ,k to ,r1 and by consequence   
out of ,glass into ,water1 as ,i to ,k3 
and let the ,diameter of the ,sphere to 
which the convex sides ,,agd and ,,chf  
are ground be ,d1 and the ,diameter of  
the ,sphere to which the concave sides  
,,bme and ,,bne1 are ground be to ,d1 as
 the ,cube ,root of ,,kk--,,ki to the   
,cube ,root of ,,rk--,,ri3 and the      
,refractions on the concave sides of the
 ,glasses1 will very much correct the   
,errors of the ,refractions on the      
convex sides1 so far as they arise from 
the sphericalness of the ,figure4 ,and  
by this means might ,telescopes be      
brought to sufficient perfection1 were  
it not for the different ,refrangibility
 of several sorts of ,rays4 ,but by     
reason of this different                
,refrangibility1 ,i do not yet see any  
other means of improving ,telescopes by 
,refractions alone1 than that of        

increasing their lengths1 for which end 
the late ,contrivance of ,hugenius seems
 well accommodated4 ,for very long      
,tubes are cumbersome1 and scarce to be 
readily managed1 and by reason of their 
length are very apt to bend1 and shake  
by bending1 so as to cause a continual  
trembling in the ,objects1 whereby it   
becomes difficult to see them           
distinctly3 whereas by his ,contrivance 
the ,glasses are readily manageable1 and
 the ,object-glass being fix'd upon a   
strong upright ,pole becomes more       
steady4  ,seeing therefore the          
,improvement of ,telescopes of given    
lengths by ,refractions is desperate2 ,i
 contrived heretofore a ,perspective by 
,reflexion1 using instead of an         
,object-glass a concave ,metal4 ,the    
diameter of the ,sphere to which the    
,metal was ground concave was about #be 
,english ,inches1 and by consequence the
 length of the ,instrument about six    
,inches and a quarter4 ,the ,eye-glass  
was ,plano-convex1 and the diameter of  

the ,sphere to which the convex side was
 ground was about #a_/e of an ,inch1 or 
a little less1 and by consequence it    
magnified between #cj and #dj times4 ,by
 another way of measuring ,i found that 
it magnified about #ce times4 ,the      
concave ,metal bore an ,aperture of an  
,inch and a third part2 but the         
,aperture was limited not by an opake   
,circle1 covering the ,limb of the      
,metal round about1 but by an opake     
,circle placed between the ,eyeglass and
 the ,eye1 and perforated in the middle 
with a little round hole for the ,rays  
to pass through to the ,eye4 ,for this  
,circle by being placed here1 stopp'd   
much of the erroneous ,light1 which     
otherwise would have disturbed the      
,vision4 ,by comparing it with a pretty 
good ,perspective of four ,feet in      
length1 made with a concave ,eye-glass1 
,i could read at a greater distance with
 my own ,instrument than with the       
,glass4 ,yet ,objects appeared much     
darker in it than in the ,glass1 and    

that partly because more ,light was lost
 by ,reflexion in the ,metal1 than by   
,refraction in the ,glass1 and partly   
because my ,instrument was overcharged4 
,had it magnified but #cj or #be times1 
it would have made the ,object appear   
more brisk and pleasant4 ,two of these  
,i made about #af ,years ago1 and have  
one of them still by me1 by which ,i can
 prove the truth of what ,i write4 ,yet 
it is not so good as at the first4 ,for 
the concave has been divers times       
tarnished and cleared again1 by rubbing 
it with very soft ,leather4 ,when ,i    
made these an ,artist in ,london        
undertook to imitate it2 but using      
another way of polishing them than ,i   
did1 he fell much short of what ,i had  
attained to1 as ,i afterwards understood
 by discoursing the ,under-workman he   
had employed4 ,the ,polish ,i used was  
in this manner4 ,i had two round ,copper
 ,plates1 each six ,inches in ,diameter1
 the one convex1 the other concave1     
ground very true to one another4 ,on the

 convex ,i ground the ,object-,metal or 
,concave which was to be polish'd1 'till
 it had taken the ,figure of the ,convex
 and was ready for a ,polish4 ,then ,i  
pitched over the convex very thinly1 by 
dropping melted ,pitch upon it1 and     
warming it to keep the ,pitch soft1     
whilst ,i ground it with the concave    
,copper wetted to make it spread eavenly
 all over the convex4 ,thus by working  
it well ,i made it as thin as a ,groat1 
and after the convex was cold ,i ground 
it again to give it as true a ,figure as
 ,i could4 ,then ,i took ,putty which ,i
 had made very fine by washing it from  
all its grosser ,particles1 and laying a
 little of this upon the ,pitch1 ,i     
ground it upon the ,pitch with the      
concave ,copper1 till it had done making
 a ,noise2 and then upon the ,pitch ,i  
ground the ,object-,metal with a brisk  
motion1 for about two or three ,minutes 
of time1 leaning hard upon it4 ,then ,i 
put fresh ,putty upon the ,pitch1 and   
ground it again till it had done making 

a noise1 and afterwards ground the      
,object-,metal upon it as before4 ,and  
this ,work ,i repeated till the ,metal  
was polished1 grinding it the last time 
with all my strength for a good while   
together1 and frequently breathing upon 
the ,pitch1 to keep it moist without    
laying on any more fresh ,putty4 ,the   
,object-,metal was two ,inches broad1   
and about one third part of an ,inch    
thick1 to keep it from bending4 ,i had  
two of these ,metals1 and when ,i had   
polished them both1 ,i tried which was  
best1 and ground the other again1 to see
 if ,i could make it better than that   
which ,i kept4 ,and thus by many ,trials
 ,i learn'd the way of polishing1 till  
,i made those two reflecting            
,perspectives ,i spake of above4 ,for   
this ,art of polishing will be better   
learn'd by repeated ,practice than by my
 ,description4 ,before ,i ground the    
,object-,metal on the ,pitch1 ,i always 
ground the ,putty on it with the concave
 ,copper1 till it had done making a     

noise1 because if the ,particles of the 
,putty were not by this means made to   
stick fast in the ,pitch1 they would by 
rolling up and down grate and fret the  
,object-,metal and fill it full of      
little holes4  ,but because ,metal is   
more difficult to polish than ,glass1   
and is afterwards very apt to be spoiled
 by tarnishing1 and reflects not so much
 ,light as ,glass quick-silver'd over   
does3 ,i would propound to use instead  
of the ,metal1 a ,glass ground concave  
on the foreside1 and as much convex on  
the backside1 and quick-silver'd over on
 the convex side4 ,the ,glass must be   
every where of the same thickness       
exactly4 ,otherwise it will make        
,objects look colour'd and indistinct4  
,by such a ,glass ,i tried about five or
 six ,years ago to make a reflecting    
,telescope of four ,feet in length to   
magnify about #aej times1 and ,i        
satisfied my self that there wants      
nothing but a good ,artist to bring the 
,design to perfection4 ,for the ,glass  

being wrought by one of our ,london     
,artists after such a manner as they    
grind ,glasses for ,telescopes1 though  
it seemed as well wrought as the        
,object-glasses use to be1 yet when it  
was quick-silver'd1 the ,reflexion      
discovered innumerable ,inequalities all
 over the ,glass4 ,and by reason of     
these ,inequalities1 ,objects appeared  
indistinct in this ,instrument4 ,for the
 ,errors of reflected ,rays caused by   
any ,inequality of the ,glass1 are about
 six times greater than the ,errors of  
refracted ,rays caused by the like      
,inequalities4 ,yet by this ,experiment 
,i satisfied my self that the ,reflexion
 on the concave side of the ,glass1     
which ,i feared would disturb the       
,vision1 did no sensible prejudice to   
it1 and by consequence that nothing is  
wanting to perfect these ,telescopes1   
but good ,workmen who can grind and     
polish ,glasses truly spherical4 ,an    
,object-glass of a fourteen ,foot       
,telescope1 made by an ,artificer at    

,london1 ,i once mended considerably1 by
 grinding it on ,pitch with ,putty1 and 
leaning very easily on it in the        
grinding1 lest the ,putty should scratch
 it4 ,whether this way may not do well  
enough for polishing these reflecting   
,glasses1 ,i have not yet tried4 ,but he
 that shall try either this or any other
 way of polishing which he may think    
better1 may do well to make his ,glasses
 ready for polishing1 by grinding them  
without that ,violence1 wherewith our   
,london ,workmen press their ,glasses in
 grinding4 ,for by such violent         
pressure1 ,glasses are apt to bend a    
little in the grinding1 and such bending
 will certainly spoil their ,figure4 ,to
 recommend therefore the consideration  
of these reflecting ,glasses to such    
,artists as are curious in figuring     
,glasses1 ,i shall describe this optical
 ,instrument in the following           
,proposition4   ,,prop4 ,,viii4 ,,prob4 
,,ii4  ,to shorten ,telescopes4  ,let   
,,abcd in ,fig4 #bi4 represent a ,glass 

spherically concave on the foreside     
,,ab1 and as much convex on the backside
 ,,cd1 so that it be every where of an  
equal thickness4 ,let it not be thicker 
on one side than on the other1 lest it  
make ,objects appear colour'd and       
indistinct1 and let it be very truly    
wrought and quick-silver'd over on the  
backside2 and set in the ,tube ,,vxyz   
which must be very black within4 ,let   
,,efg represent a ,prism of ,glass or   
,crystal placed near the other end of   
the ,tube1 in the middle of it1 by means
 of a handle of ,brass or ,iron ,,fgk1  
to the end of which made flat it is     
cemented4 ,let this ,prism be           
rectangular at ,e1 and let the other two
 ,angles at ,f and ,g be accurately     
equal to each other1 and by consequence 
equal to half right ones1 and let the   
plane sides ,,fe and ,,ge be square1 and
 by consequence the third side ,,fg a   
rectangular ,parallelogram1 whose length
 is to its breadth in a subduplicate    
proportion of two to one4 ,let it be so 

placed in the ,tube1 that the ,axis of  
the ,speculum may pass through the      
middle of the square side ,,ef          
perpendicularly and by consequence      
through the middle of the side ,,fg at  
an ,angle of #de ,degrees1 and let the  
side ,,ef be turned towards the         
,speculum1 and the distance of this     
,prism from the ,speculum be such that  
the ,rays of the ,light ,,pq1 ,,rs1 c4  
which are incident upon the ,speculum in
 ,lines parallel to the ,axis thereof1  
may enter the ,prism at the side ,,ef1  
and be reflected by the side ,,fg1 and  
thence go out of it through the side    
,,ge1 to the ,point ,t1 which must be   
the common ,focus of the ,speculum      
,,abdc1 and of a ,plano-convex          
,eye-glass ,h1 through which those ,rays
 must pass to the ,eye4 ,and let the    
,rays at their coming out of the ,glass 
pass through a small round hole1 or     
aperture made in a little plate of      
,lead1 ,brass1 or ,silver1 wherewith the
 ,glass is to be covered1 which hole    

must be no bigger than is necessary for 
,light enough to pass through4 ,for so  
it will render the ,object distinct1 the
 ,plate in which 'tis made intercepting 
all the erroneous part of the ,light    
which comes from the verges of the      
,speculum ,,ab4 ,such an ,instrument    
well made1 if it be six ,foot long1     
7reckoning the length from the ,speculum
 to the ,prism1 and thence to the ,focus
 ,t7 will bear an aperture of six       
,inches at the ,speculum1 and magnify   
between two and three hundred times4    
,but the hole ,h here limits the        
aperture with more advantage1 than if   
the aperture was placed at the          
,speculum4 ,if the ,instrument be made  
longer or shorter1 the aperture must be 
in proportion as the ,cube of the       
square-square ,root of the length1 and  
the magnifying as the aperture4 ,but    
it's convenient that the ,speculum be an
 ,inch or two broader than the aperture 
at the least1 and that the ,glass of the
 ,speculum be thick1 that it bend not in

 the working4 ,the ,prism ,,efg must be 
no bigger than is necessary1 and its    
back side ,,fg must not be              
quick-silver'd over4 ,for without       
quicksilver it will reflect all the     
,light incident on it from the          
,speculum4  ,illustration3 ,,fig4 #bi4  
,in this ,instrument the ,object will be
 inverted1 but may be erected by making 
the square sides ,,ff and ,,eg of the   
,prism ,,efg not plane but spherically  
convex1 that the ,rays may cross as well
 before they come at it as afterwards   
between it and the ,eye-glass4 ,if it be
 desired that the ,instrument bear a    
larger aperture1 that may be also done  
by composing the ,speculum of two       
,glasses with ,water between them4  ,if 
the ,theory of making ,telescopes could 
at length be fully brought into         
,practice1 yet there would be certain   
,bounds beyond which ,telescopes could  
not perform4 ,for the ,air through which
 we look upon the ,stars1 is in a       
perpetual ,tremor2 as may be seen by the

 tremulous ,motion of ,shadows cast from
 high ,towers1 and by the twinkling of  
the fix'd ,stars4 ,but these ,stars do  
not twinkle when viewed through         
,telescopes which have large apertures4 
,for the ,rays of ,light which pass     
through divers parts of the aperture1   
tremble each of them apart1 and by means
 of their various and sometimes contrary
 ,tremors1 fall at one and the same time
 upon different points in the bottom of 
the ,eye1 and their trembling ,motions  
are too quick and confused to be        
perceived severally4 ,and all these     
illuminated ,points constitute one broad
 lucid ,point1 composed of those many   
trembling ,points confusedly and        
insensibly mixed with one another by    
very short and swift ,tremors1 and      
thereby cause the ,star to appear       
broader than it is1 and without any     
trembling of the whole4 ,long           
,telescopes may cause ,objects to appear
 brighter and larger than short ones can
 do1 but they cannot be so formed as to 

take away that confusion of the ,rays   
which arises from the ,tremors of the   
,atmosphere4 ,the only ,remedy is a most
 serene and quiet ,air1 such as may     
perhaps be found on the tops of the     
highest ,mountains above the grosser    
,clouds4  ,,footnotes3  ,c ,see our     
,author's ,lectiones ,opticae ,sec4 #aj4
 ,sect4 ,,ii4 ,sec4 #bi4 and ,sect4     
,,iii4 ,prop4 #be4  ,d ,see our         
,author's ,lectiones ,opticae1 ,part4   
,i4 ,sect4 #a4 ,sec4#e4  ,e ,this is    
very fully treated of in our ,author's  
,lect4 ,optic4 ,part ,i4 ,sect4 ,,ii4   
,f ,see our ,author's ,lect4 ,optic4    
,part ,i4 ,sect4 ,,ii4 ,sec4 #bi4  ,g   
,this is demonstrated in our ,author's  
,lect4 ,optic4 ,part ,i4 ,sect4 ,,iv4   
,prop4 #cg4  ,h ,how to do this1 is     
shewn in our ,author's ,lect4 ,optic4   
,part ,i4 ,sect4 ,,iv4 ,prop4 #ca4      
,,the ,,first ,,book ,,of ,,opticks     
,,part ,,ii4   ,,prop4 ,i4 ,,theor4 ,i4 
,the ,phaenomena of ,colours in         
refracted or reflected ,light are not   

caused by new ,modifications of the     
,light variously impress'd1 according to
 the various ,terminations of the ,light
 and ,shadow4  ,the ,,proof by          
,experiments4  ,exper4 #a4 ,for if the  
,sun shine into a very dark ,chamber    
through an oblong hole ,f1 in ,fig4 #a4 
whose breadth is the sixth or eighth    
part of an ,inch1 or something less2 and
 his beam ,,fh do afterwards pass first 
through a very large ,prism ,,abc1      
distant about #bj ,feet from the hole1  
and parallel to it1 and then 7with its  
white part7 through an oblong hole ,h1  
whose breadth is about the fortieth or  
sixtieth part of an ,inch1 and which is 
made in a black opake ,body ,,gi1 and   
placed at the distance of two or three  
,feet from the ,prism1 in a parallel    
,situation both to the ,prism and to the
 former hole1 and if this white ,light  
thus transmitted through the hole ,h1   
fall afterwards upon a white ,paper pt1 
placed after that hole ,h1 at the       
distance of three or four ,feet from it1

 and there paint the usual ,colours of  
the ,prism1 suppose red at t1 yellow at 
s1 green at r1 blue at q1 and violet at 
p2 you may with an ,iron ,wire1 or any  
such like slender opake ,body1 whose    
breadth is about the tenth part of an   
,inch1 by intercepting the ,rays at k1  
l1 m1 n or o1 take away any one of the  
,colours at t1 s1 r1 q or p1 whilst the 
other ,colours remain upon the ,paper as
 before2 or with an ,obstacle something 
bigger you may take away any two1 or    
three1 or four ,colours together1 the   
rest remaining3 ,so that any one of the 
,colours as well as violet may become   
outmost in the ,confine of the ,shadow  
towards p1 and any one of them as well  
as red may become outmost in the        
,confine of the ,shadow towards t1 and  
any one of them may also border upon the
 ,shadow made within the ,colours by the
 ,obstacle ,r intercepting some         
intermediate part of the ,light2 and1   
lastly1 any one of them by being left   
alone1 may border upon the ,shadow on   

either hand4 ,all the ,colours have     
themselves indifferently to any         
,confines of ,shadow1 and therefore the 
differences of these ,colours from one  
another1 do not arise from the different
 ,confines of ,shadow1 whereby ,light is
 variously modified1 as has hitherto    
been the ,opinion of ,philosophers4 ,in 
trying these things 'tis to be observed1
 that by how much the holes ,f and ,h   
are narrower1 and the ,intervals between
 them and the ,prism greater1 and the   
,chamber darker1 by so much the better  
doth the ,experiment succeed2 provided  
the ,light be not so far diminished1 but
 that the ,colours at pt be sufficiently
 visible4 ,to procure a ,prism of solid 
,glass large enough for this ,experiment
 will be difficult1 and therefore a     
prismatick ,vessel must be made of      
polish'd ,glass ,plates cemented        
together1 and filled with salt ,water or
 clear ,oil4  ,illustration3 ,,fig4 #a4 
,exper4 #b4 ,the ,sun's ,light let into 
a dark ,chamber through the round hole  

,f1 in ,fig4 #b4 half an ,inch wide1    
passed first through the ,prism ,,abc   
placed at the hole1 and then through a  
,lens ,,pt something more than four     
,inches broad1 and about eight ,feet    
distant from the ,prism1 and thence     
converged to ,o the ,focus of the ,lens 
distant from it about three ,feet1 and  
there fell upon a white ,paper ,,de4 ,if
 that ,paper was perpendicular to that  
,light incident upon it1 as 'tis        
represented in the posture ,,de1 all the
 ,colours upon it at ,o appeared white4 
,but if the ,paper being turned about an
 ,axis parallel to the ,prism1 became   
very much inclined to the ,light1 as    
'tis represented in the ,positions de   
and ,greek3 de2 the same ,light in the  
one case appeared yellow and red1 in the
 other blue4 ,here one and the same part
 of the ,light in one and the same      
place1 according to the various         
,inclinations of the ,paper1 appeared in
 one case white1 in another yellow or   
red1 in a third blue1 whilst the        

,confine of ,light and shadow1 and the  
,refractions of the ,prism in all these 
cases remained the same4  ,illustration3
 ,,fig4 #b4  ,illustration3 ,,fig4 #c4  
,exper4 #c4 ,such another ,experiment   
may be more easily tried as follows4    
,let a broad beam of the ,sun's ,light  
coming into a dark ,chamber through a   
hole in the ,window-shut be refracted by
 a large ,prism ,,abc1 in ,fig4 #c4     
whose refracting ,angle ,c is more than 
#fj ,degrees1 and so soon as it comes   
out of the ,prism1 let it fall upon the 
white ,paper ,,de glewed upon a stiff   
,plane2 and this ,light1 when the ,paper
 is perpendicular to it1 as 'tis        
represented in ,,de1 will appear        
perfectly white upon the ,paper2 but    
when the ,paper is very much inclin'd to
 it in such a manner as to keep always  
parallel to the ,axis of the ,prism1 the
 whiteness of the whole ,light upon the 
,paper will according to the inclination
 of the ,paper this way or that way1    
change either into yellow and red1 as in

 the posture de1 or into blue and       
violet1 as in the posture ,greek3 de4   
,and if the ,light before it fall upon  
the ,paper be twice refracted the same  
way by two parallel ,prisms1 these      
,colours will become the more           
conspicuous4 ,here all the middle parts 
of the broad beam of white ,light which 
fell upon the ,paper1 did without any   
,confine of ,shadow to modify it1 become
 colour'd all over with one uniform     
,colour1 the ,colour being always the   
same in the middle of the ,paper as at  
the edges1 and this ,colour changed     
according to the various ,obliquity of  
the reflecting ,paper1 without any      
change in the ,refractions or ,shadow1  
or in the ,light which fell upon the    
,paper4 ,and therefore these ,colours   
are to be derived from some other ,cause
 than the new ,modifications of ,light  
by ,refractions and ,shadows4  ,if it be
 asked1 what then is their ,cause8 ,i   
answer1 ,that the ,paper in the posture 
de1 being more oblique to the more      

refrangible ,rays than to the less      
refrangible ones1 is more strongly      
illuminated by the latter than by the   
former1 and therefore the less          
refrangible ,rays are predominant in the
 reflected ,light4 ,and where-ever they 
are predominant in any ,light1 they     
tinge it with red or yellow1 as may in  
some measure appear by the first        
,proposition of the first ,part of this 
,book1 and will more fully appear       
hereafter4 ,and the contrary happens in 
the posture of the ,paper ,greek3 de1   
the more refrangible ,rays being then   
predominant which always tinge ,light   
with blues and violets4  ,exper4 #d4    
,the ,colours of ,bubbles with which    
,children play are various1 and change  
their ,situation variously1 without any 
respect to any ,confine or ,shadow4 ,if 
such a ,bubble be cover'd with a concave
 ,glass1 to keep it from being agitated 
by any ,wind or ,motion of the ,air1 the
 ,colours will slowly and regularly     
change their situation1 even whilst the 

,eye and the ,bubble1 and all ,bodies   
which emit any ,light1 or cast any      
,shadow1 remain unmoved4 ,and therefore 
their ,colours arise from some regular  
,cause which depends not on any ,confine
 of ,shadow4 ,what this ,cause is will  
be shewed in the next ,book4  ,to these 
,experiments may be added the tenth     
,experiment of the first ,part of this  
first ,book1 where the ,sun's ,light in 
a dark ,room being trajected through the
 parallel ,superficies of two ,prisms   
tied together in the form of a          
,parallelopipede1 became totally of one 
uniform yellow or red ,colour1 at its   
emerging out of the ,prisms4 ,here1 in  
the production of these ,colours1 the   
,confine of ,shadow can have nothing to 
do4 ,for the ,light changes from white  
to yellow1 orange and red successively1 
without any alteration of the ,confine  
of ,shadow3 ,and at both edges of the   
emerging ,light where the contrary      
,confines of ,shadow ought to produce   
different ,effects1 the ,colour is one  

and the same1 whether it be white1      
yellow1 orange or red3 ,and in the      
middle of the emerging ,light1 where    
there is no ,confine of ,shadow at all1 
the ,colour is the very same as at the  
edges1 the whole ,light at its very     
first ,emergence being of one uniform   
,colour1 whether white1 yellow1 orange  
or red1 and going on thence perpetually 
without any change of ,colour1 such as  
the ,confine of ,shadow is vulgarly     
supposed to work in refracted ,light    
after its ,emergence4 ,neither can these
 ,colours arise from any new            
,modifications of the ,light by         
,refractions1 because they change       
successively from white to yellow1      
orange and red1 while the ,refractions  
remain the same1 and also because the   
,refractions are made contrary ways by  
parallel ,superficies which destroy one 
another's ,effects4 ,they arise not     
therefore from any ,modifications of    
,light made by ,refractions and         
,shadows1 but have some other ,cause4   

,what that ,cause is we shewed above in 
this tenth ,experiment1 and need not    
here repeat it4  ,there is yet another  
material ,circumstance of this          
,experiment4 ,for this emerging ,light  
being by a third ,prism ,,hik in ,fig4  
#bb4 ,part ,i4,i refracted towards the  
,paper ,,pt1 and there painting the     
usual ,colours of the ,prism1 red1      
yellow1 green1 blue1 violet3 ,if these  
,colours arose from the ,refractions of 
that ,prism modifying the ,light1 they  
would not be in the ,light before its   
,incidence on that ,prism4 ,and yet in  
that ,experiment we found1 that when by 
turning the two first ,prisms about     
their common ,axis all the ,colours were
 made to vanish but the red2 the ,light 
which makes that red being left alone1  
appeared of the very same red ,colour   
before its ,incidence on the third      
,prism4 ,and in general we find by other
 ,experiments1 that when the ,rays which
 differ in ,refrangibility are separated
 from one another1 and any one ,sort of 

them is considered apart1 the ,colour of
 the ,light which they compose cannot be
 changed by any ,refraction or          
,reflexion whatever1 as it ought to be  
were ,colours nothing else than         
,modifications of ,light caused by      
,refractions1 and ,reflexions1 and      
,shadows4 ,this ,unchangeableness of    
,colour ,i am now to describe in the    
following ,proposition4   ,,prop4 ,,ii4 
,,theor4 ,,ii4  ,all homogeneal ,light  
has its proper ,colour answering to its 
,degree of ,refrangibility1 and that    
,colour cannot be changed by ,reflexions
 and ,refractions4  ,in the ,experiments
 of the fourth ,proposition of the first
 ,part of this first ,book1 when ,i had 
separated the heterogeneous ,rays from  
one another1 the ,spectrum pt formed by 
the separated ,rays1 did in the         
,progress from its ,end p1 on which the 
most refrangible ,rays fell1 unto its   
other ,end t1 on which the least        
refrangible ,rays fell1 appear tinged   
with this ,series of ,colours1 violet1  

indigo1 blue1 green1 yellow1 orange1    
red1 together with all their            
intermediate ,degrees in a continual    
,succession perpetually varying4 ,so    
that there appeared as many ,degrees of 
,colours1 as there were sorts of ,rays  
differing in ,refrangibility4  ,exper4  
#e4 ,now1 that these ,colours could not 
be changed by ,refraction1 ,i knew by   
refracting with a ,prism sometimes one  
very little ,part of this ,light1       
sometimes another very little ,part1 as 
is described in the twelfth ,experiment 
of the first ,part of this ,book4 ,for  
by this ,refraction the ,colour of the  
,light was never changed in the least4  
,if any ,part of the red ,light was     
refracted1 it remained totally of the   
same red ,colour as before4 ,no orange1 
no yellow1 no green or blue1 no other   
new ,colour was produced by that        
,refraction4 ,neither did the ,colour   
any ways change by repeated             
,refractions1 but continued always the  
same red entirely as at first4 ,the like

 ,constancy and ,immutability ,i found  
also in the blue1 green1 and other      
,colours4 ,so also1 if ,i looked through
 a ,prism upon any ,body illuminated    
with any part of this homogeneal ,light1
 as in the fourteenth ,experiment of the
 first ,part of this ,book is described2
 ,i could not perceive any new ,colour  
generated this way4 ,all ,bodies        
illuminated with compound ,light appear 
through ,prisms confused1 7as was said  
above7 and tinged with various new      
,colours1 but those illuminated with    
homogeneal ,light appeared through      
,prisms neither less distinct1 nor      
otherwise colour'd1 than when viewed    
with the naked ,eyes4 ,their ,colours   
were not in the least changed by the    
,refraction of the interposed ,prism4 ,i
 speak here of a sensible ,change of    
,colour3 ,for the ,light which ,i here  
call homogeneal1 being not absolutely   
homogeneal1 there ought to arise some   
little ,change of ,colour from its      
,heterogeneity4 ,but1 if that           

,heterogeneity was so little as it might
 be made by the said ,experiments of the
 fourth ,proposition1 that ,change was  
not sensible1 and therefore in          
,experiments1 where ,sense is ,judge1   
ought to be accounted none at all4      
,exper4 #f4 ,and as these ,colours were 
not changeable by ,refractions1 so      
neither were they by ,reflexions4 ,for  
all white1 grey1 red1 yellow1 green1    
blue1 violet ,bodies1 as ,paper1 ,ashes1
 red ,lead1 ,orpiment1 ,indico ,bise1   
,gold1 ,silver1 ,copper1 ,grass1 blue   
,flowers1 ,violets1 ,bubbles of ,water  
tinged with various ,colours1 ,peacock's
 ,feathers1 the ,tincture of ,lignum    
,nephriticum1 and such-like1 in red     
homogeneal ,light appeared totally red1 
in blue ,light totally blue1 in green   
,light totally green1 and so of other   
,colours4 ,in the homogeneal ,light of  
any ,colour they all appeared totally of
 that same ,colour1 with this only      
,difference1 that some of them reflected
 that ,light more strongly1 others more 

faintly4 ,i never yet found any ,body1  
which by reflecting homogeneal ,light   
could sensibly change its ,colour4      
,from all which it is manifest1 that if 
the ,sun's ,light consisted of but one  
sort of ,rays1 there would be but one   
,colour in the whole ,world1 nor would  
it be possible to produce any new       
,colour by ,reflexions and ,refractions1
 and by consequence that the variety of 
,colours depends upon the ,composition  
of ,light4   ,,definition4  ,the        
homogeneal ,light and ,rays which appear
 red1 or rather make ,objects appear so1
 ,i call ,rubrifick or ,red-making2     
those which make ,objects appear yellow1
 green1 blue1 and violet1 ,i call       
,yellow-making1 ,green-making1          
,blue-making1 ,violet-making1 and so of 
the rest4 ,and if at any time ,i speak  
of ,light and ,rays as coloured or      
endued with ,colours1 ,i would be       
understood to speak not philosophically 
and properly1 but grossly1 and          
accordingly to such ,conceptions as     

vulgar ,people in seeing all these      
,experiments would be apt to frame4 ,for
 the ,rays to speak properly are not    
coloured4 ,in them there is nothing else
 than a certain ,power and ,disposition 
to stir up a ,sensation of this or that 
,colour4 ,for as ,sound in a ,bell or   
musical ,string1 or other sounding      
,body1 is nothing but a trembling       
,motion1 and in the ,air nothing but    
that ,motion propagated from the        
,object1 and in the ,sensorium 'tis a   
,sense of that ,motion under the ,form  
of ,sound2 so ,colours in the ,object   
are nothing but a ,disposition to       
reflect this or that sort of ,rays more 
copiously than the rest2 in the ,rays   
they are nothing but their ,dispositions
 to propagate this or that ,motion into 
the ,sensorium1 and in the ,sensorium   
they are ,sensations of those ,motions  
under the ,forms of ,colours4   ,,prop4 
,,iii4 ,,prob4 ,i4  ,to define the      
,refrangibility of the several sorts of 
homogeneal ,light answering to the      

several ,colours4  ,for determining this
 ,problem ,i made the following         
,experiment4,j  ,exper4 #g4 ,when ,i had
 caused the ,rectilinear ,sides ,,af1   
,,gm1 in ,fig4 #d4 of the ,spectrum of  
,colours made by the ,prism to be       
distinctly defined1 as in the fifth     
,experiment of the first ,part of this  
,book is described1 there were found in 
it all the homogeneal ,colours in the   
same ,order and ,situation one among    
another as in the ,spectrum of simple   
,light1 described in the fourth         
,proposition of that ,part4 ,for the    
,circles of which the ,spectrum of      
compound ,light ,,pt is composed1 and   
which in the middle ,parts of the       
,spectrum interfere1 and are intermix'd 
with one another1 are not intermix'd in 
their outmost ,parts where they touch   
those ,rectilinear ,sides ,,af and ,,gm4
 ,and therefore1 in those ,rectilinear  
,sides when distinctly defined1 there is
 no new ,colour generated by            
,refraction4 ,i observed also1 that if  

any where between the two outmost       
,circles ,,tmf and ,,pga a ,right ,line1
 as ,greek3 gd1 was cross to the        
,spectrum1 so as both ,ends to fall     
perpendicularly upon its ,rectilinear   
,sides1 there appeared one and the same 
,colour1 and degree of ,colour from one 
,end of this ,line to the other4 ,i     
delineated therefore in a ,paper the    
,perimeter of the ,spectrum ,,fap ,,gmt1
 and in trying the third ,experiment of 
the first ,part of this ,book1 ,i held  
the ,paper so that the ,spectrum might  
fall upon this delineated ,figure1 and  
agree with it exactly1 whilst an        
,assistant1 whose ,eyes for             
distinguishing ,colours were more       
critical than mine1 did by ,right ,lines
 ,greek3 ab1 gd1 ez1 c4 drawn cross the 
,spectrum1 note the ,confines of the    
,colours1 that is of the red ,m,greek3  
ab,f1 of the orange ,greek3 agdb1 of the
 yellow ,greek3 gezd1 of the green      
,greek3 eethz1 of the blue ,greek3      
eikth1 of the indico ,greek3 ilmk1 and  

of the violet ,greek3 l,,ga,greek3 m4   
,and this ,operation being divers times 
repeated both in the same1 and in       
several ,papers1 ,i found that the      
,observations agreed well enough with   
one another1 and that the ,rectilinear  
,sides ,,mg and ,,fa were by the said   
cross ,lines divided after the manner of
 a ,musical ,chord4 ,let ,,gm be        
produced to ,x1 that ,,mx may be equal  
to ,,gm1 and conceive ,,gx1 ,greek3 l,x1
 ,greek3 i,x1 ,greek3 e,x1 ,greek3 e,x1 
,greek3 g,x1 ,greek3 a,x1 ,,mx1 to be in
 proportion to one another1 as the      
,numbers1 #a1 #h_/i1 #e_/f1 #c_/d1      
#b_/c1 #c_/e1 #i_/af1 #a_/b1 and so to  
represent the ,chords of the ,key1 and  
of a ,tone1 a third ,minor1 a fourth1 a 
fifth1 a sixth ,major1 a seventh and an 
eighth above that ,key3 ,and the        
,intervals ,m,greek3 a1 ,greek3 ag1     
,greek3 ge1 ,greek3 ee1 ,greek3 ei1     
,greek3 il1 and ,greek3 l,g1 will be the
 ,spaces which the several ,colours     
7red1 orange1 yellow1 green1 blue1      

indigo1 violet7 take up4  ,illustration3
 ,,fig4 #d4  ,illustration3 ,,fig4 #e4  
,now these ,intervals or ,spaces        
subtending the ,differences of the      
,refractions of the ,rays going to the  
,limits of those ,colours1 that is1 to  
the ,points ,m1 ,greek3 a1 ,greek3 g1   
,greek3 e1 ,greek3 e1 ,greek3 i1 ,greek3
 l1 ,g1 may without any sensible ,error 
be accounted proportional to the        
,differences of the ,sines of           
,refraction of those ,rays having one   
common ,sine of ,incidence1 and         
therefore since the common ,sine of     
,incidence of the most and least        
refrangible ,rays out of ,glass into    
,air was 7by a ,method described above7 
found in proportion to their ,sines of  
,refraction1 as #ej to #gg and #gh1     
divide the ,difference between the      
,sines of ,refraction #gg and #gh1 as   
the ,line ,,gm is divided by those      
,intervals1 and you will have #gg1      
#gg-a_/h1 #gg-a_/e1 #gg-a_/c1 #gg-a_/b1 
#gg-b_/c1 #gg-g_/i1 #gh1 the ,sines of  

,refraction of those ,rays out of ,glass
 into ,air1 their common ,sine of       
,incidence being #ej4 ,so then the      
,sines of the ,incidences of all the    
red-making ,rays out of ,glass into     
,air1 were to the ,sines of their       
,refractions1 not greater than #ej to   
#gg1 nor less than #ej to #gg-a_/h1 but 
they varied from one another according  
to all intermediate ,proportions4 ,and  
the ,sines of the ,incidences of the    
green-making ,rays were to the ,sines of
 their ,refractions in all ,proportions 
from that of #ej to #gg-a_/c1 unto that 
of #ej to #gg-a_/b4 ,and by the like    
,limits above-mentioned were the        
,refractions of the ,rays belonging to  
the rest of the ,colours defined1 the   
,sines of the red-making ,rays extending
 from #gg to #gg-a_/h1 those of the     
orange-making from #gg-a_/h to #gg-a_/e1
 those of the yellow-making from        
#gg-a_/e to #gg-a_/c1 those of the      
green-making from #gg-a_/c to #gg-a_/b1 
those of the blue-making from #gg-a_/b  

to #gg-b_/c1 those of the indigo-making 
from #gg-b_/c to #gg-g_/i1 and those of 
the violet from #gg-g_/i1 to #gh4       
,these are the ,laws of the ,refractions
 made out of ,glass into ,air1 and      
thence by the third ,axiom of the first 
,part of this ,book1 the ,laws of the   
,refractions made out of ,air into      
,glass are easily derived4  ,exper4 #h4 
,i found moreover1 that when ,light goes
 out of ,air through several contiguous 
refracting ,mediums as through ,water   
and ,glass1 and thence goes out again   
into ,air1 whether the refracting       
,superficies be parallel or inclin'd to 
one another1 that ,light as often as by 
contrary ,refractions 'tis so corrected1
 that it emergeth in ,lines parallel to 
those in which it was incident1         
continues ever after to be white4 ,but  
if the emergent ,rays be inclined to the
 incident1 the ,whiteness of the        
emerging ,light will by degrees in      
passing on from the ,place of           
,emergence1 become tinged in its ,edges 

with ,colours4 ,this ,i try'd by        
refracting ,light with ,prisms of ,glass
 placed within a ,prismatick ,vessel of 
,water4 ,now those ,colours argue a     
diverging and separation of the         
heterogeneous ,rays from one another by 
means of their unequal ,refractions1 as 
in what follows will more fully appear4 
,and1 on the contrary1 the permanent    
whiteness argues1 that in like          
,incidences of the ,rays there is no    
such separation of the emerging ,rays1  
and by consequence no inequality of     
their whole ,refractions4 ,whence ,i    
seem to gather the two following        
,theorems4  #a4 ,the ,excesses of the   
,sines of ,refraction of several sorts  
of ,rays above their common ,sine of    
,incidence when the ,refractions are    
made out of divers denser ,mediums      
immediately into one and the same rarer 
,medium1 suppose of ,air1 are to one    
another in a given ,proportion4  #b4    
,the ,proportion of the ,sine of        
,incidence to the ,sine of ,refraction  

of one and the same sort of ,rays out of
 one ,medium into another1 is composed  
of the ,proportion of the ,sine of      
,incidence to the ,sine of ,refraction  
out of the first ,medium into any third 
,medium1 and of the ,proportion of the  
,sine of ,incidence to the ,sine of     
,refraction out of that third ,medium   
into the second ,medium4  ,by the first 
,theorem the ,refractions of the ,rays  
of every sort made out of any ,medium   
into ,air are known by having the       
,refraction of the ,rays of any one     
sort4 ,as for instance1 if the          
,refractions of the ,rays of every sort 
out of ,rain-water into ,air be desired1
 let the common ,sine of ,incidence out 
of ,glass into ,air be subducted from   
the ,sines of ,refraction1 and the      
,excesses will be #bg1 #bg-a_/h1        
#bg-a_/e1 #bg-a_/c1 #bg-a_/b1 #bg-b_/c1 
#bg-g_/i1 #bh4 ,suppose now that the    
,sine of ,incidence of the least        
refrangible ,rays be to their ,sine of  
,refraction out of ,rain-water into ,air

 as #c to #d1 and say as #a the         
difference of those ,sines is to #c the 
,sine of ,incidence1 so is #bg the least
 of the ,excesses above-mentioned to a  
fourth ,number #ha2 and #ha will be the 
common ,sine of ,incidence out of       
,rain-water into ,air1 to which ,sine if
 you add all the above-mentioned        
,excesses1 you will have the desired    
,sines of the ,refractions #ajh1        
#ajh-a_/h1 #ajh-a_/e1 #ajh-a_/c1        
#ajh-a_/b1 #ajh-b_/c1 #ajh-g_/i1 #aji4  
,by the latter ,theorem the ,refraction 
out of one ,medium into another is      
gathered as often as you have the       
,refractions out of them both into any  
third ,medium4 ,as if the ,sine of      
,incidence of any ,ray out of ,glass    
into ,air be to its ,sine of            
,refraction1 as #bj to #ca1 and the     
,sine of ,incidence of the same ,ray out
 of ,air into ,water1 be to its ,sine of
 ,refraction as #d to #c2 the ,sine of  
,incidence of that ,ray out of ,glass   
into ,water will be to its ,sine of     

,refraction as #bj to #ca and #d to #c  
jointly1 that is1 as the ,factum of #bj 
and #d to the ,factum of #ca and #c1 or 
as #hj to #ic4  ,and these ,theorems    
being admitted into ,opticks1 there     
would be scope enough of handling that  
,science voluminously after a new       
manner1,k not only by teaching those    
things which tend to the perfection of  
,vision1 but also by determining        
mathematically all kinds of ,phaenomena 
of ,colours which could be produced by  
,refractions4 ,for to do this1 there is 
nothing else requisite than to find out 
the ,separations of heterogeneous ,rays1
 and their various ,mixtures and        
,proportions in every ,mixture4 ,by this
 way of arguing ,i invented almost all  
the ,phaenomena described in these      
,books1 beside some others less         
necessary to the ,argument2 and by the  
successes ,i met with in the ,trials1 ,i
 dare promise1 that to him who shall    
argue truly1 and then try all things    
with good ,glasses and sufficient       

,circumspection1 the expected ,event    
will not be wanting4 ,but he is first to
 know what ,colours will arise from any 
others mix'd in any assigned            
,proportion4   ,,prop4 ,,iv4 ,,theor4   
,,iii4  ,colours may be produced by     
,composition which shall be like to the 
,colours of homogeneal ,light as to the 
,appearance of ,colour1 but not as to   
the ,immutability of ,colour and        
,constitution of ,light4 ,and those     
,colours by how much they are more      
compounded by so much are they less full
 and intense1 and by too much           
,composition they maybe diluted and     
weaken'd till they cease1 and the       
,mixture becomes white or grey4 ,there  
may be also ,colours produced by        
,composition1 which are not fully like  
any of the ,colours of homogeneal       
,light4  ,for a ,mixture of homogeneal  
red and yellow compounds an ,orange1    
like in appearance of ,colour to that   
orange which in the series of unmixed   
prismatick ,colours lies between them2  

but the ,light of one orange is         
homogeneal as to ,refrangibility1 and   
that of the other is heterogeneal1 and  
the ,colour of the one1 if viewed       
through a ,prism1 remains unchanged1    
that of the other is changed and        
resolved into its component ,colours red
 and yellow4 ,and after the same manner 
other neighbouring homogeneal ,colours  
may compound new ,colours1 like the     
intermediate homogeneal ones1 as yellow 
and green1 the ,colour between them     
both1 and afterwards1 if blue be added1 
there will be made a green the middle   
,colour of the three which enter the    
,composition4 ,for the yellow and blue  
on either hand1 if they are equal in    
quantity they draw the intermediate     
green equally towards themselves in     
,composition1 and so keep it as it were 
in ,a,equilibrion1 that it verge not    
more to the yellow on the one hand1 and 
to the blue on the other1 but by their  
mix'd ,actions remain still a middle    
,colour4 ,to this mix'd green there may 

be farther added some red and violet1   
and yet the green will not presently    
cease1 but only grow less full and      
vivid1 and by increasing the red and    
violet1 it will grow more and more      
dilute1 until by the prevalence of the  
added ,colours it be overcome and turned
 into whiteness1 or some other ,colour4 
,so if to the ,colour of any homogeneal 
,light1 the ,sun's white ,light composed
 of all sorts of ,rays be added1 that   
,colour will not vanish or change its   
,species1 but be diluted1 and by adding 
more and more white it will be diluted  
more and more perpetually4 ,lastly1 ,if 
red and violet be mingled1 there will be
 generated according to their various   
,proportions various ,purples1 such as  
are not like in appearance to the       
,colour of any homogeneal ,light1 and of
 these ,purples mix'd with yellow and   
blue may be made other new ,colours4    
,,prop4 ,v4 ,,theor4 ,,iv4  ,whiteness  
and all grey ,colours between white and 
black1 may be compounded of ,colours1   

and the whiteness of the ,sun's ,light  
is compounded of all the primary        
,colours mix'd in a due ,proportion4    
,the ,,proof by ,experiments4  ,exper4  
#i4 ,the ,sun shining into a dark       
,chamber through a little round hole in 
the ,window-shut1 and his ,light being  
there refracted by a ,prism to cast his 
coloured ,image ,,pt in ,fig4 #e4 upon  
the opposite ,wall3 ,i held a white     
,paper ,v to that image in such manner  
that it might be illuminated by the     
colour'd ,light reflected from thence1  
and yet not intercept any part of that  
,light in its passage from the ,prism to
 the ,spectrum4 ,and ,i found that when 
the ,paper was held nearer to any       
,colour than to the rest1 it appeared of
 that ,colour to which it approached    
nearest2 but when it was equally or     
almost equally distant from all the     
,colours1 so that it might be equally   
illuminated by them all it appeared     
white4 ,and in this last situation of   
the ,paper1 if some ,colours were       

intercepted1 the ,paper lost its white  
,colour1 and appeared of the ,colour of 
the rest of the ,light which was not    
intercepted4 ,so then the ,paper was    
illuminated with ,lights of various     
,colours1 namely1 red1 yellow1 green1   
blue and violet1 and every part of the  
,light retained its proper ,colour1     
until it was incident on the ,paper1 and
 became reflected thence to the ,eye2 so
 that if it had been either alone 7the  
rest of the ,light being intercepted7 or
 if it had abounded most1 and been      
predominant in the ,light reflected from
 the ,paper1 it would have tinged the   
,paper with its own ,colour2 and yet    
being mixed with the rest of the        
,colours in a due proportion1 it made   
the ,paper look white1 and therefore by 
a ,composition with the rest produced   
that ,colour4 ,the several parts of the 
coloured ,light reflected from the      
,spectrum1 whilst they are propagated   
from thence through the ,air1 do        
perpetually retain their proper         

,colours1 because wherever they fall    
upon the ,eyes of any ,spectator1 they  
make the several parts of the ,spectrum 
to appear under their proper ,colours4  
,they retain therefore their proper     
,colours when they fall upon the ,paper 
,v1 and so by the confusion and perfect 
mixture of those ,colours compound the  
whiteness of the ,light reflected from  
thence4  ,exper4 #aj4 ,let that         
,spectrum or solar ,image ,,pt in ,fig4 
#f4 fall now upon the ,lens ,,mn above  
four ,inches broad1 and about six ,feet 
distant from the ,prism ,,abc and so    
figured that it may cause the coloured  
,light which divergeth from the ,prism  
to converge and meet again at its ,focus
 ,g1 about six or eight ,feet distant   
from the ,lens1 and there to fall       
perpendicularly upon a white ,paper     
,,de4 ,and if you move this ,paper to   
and fro1 you will perceive that near the
 ,lens1 as at de1 the whole solar ,image
 7suppose at pt7 will appear upon it    
intensely coloured after the manner     

above-explained1 and that by receding   
from the ,lens those ,colours will      
perpetually come towards one another1   
and by mixing more and more dilute one  
another continually1 until at length the
 ,paper come to the ,focus ,g1 where by 
a perfect mixture they will wholly      
vanish and be converted into whiteness1 
the whole ,light appearing now upon the 
,paper like a little white ,circle4 ,and
 afterwards by receding farther from the
 ,lens1 the ,rays which before converged
 will now cross one another in the      
,focus ,g1 and diverge from thence1 and 
thereby make the ,colours to appear     
again1 but yet in a contrary order2     
suppose at ,greek3 de1 where the red t  
is now above which before was below1 and
 the violet p is below which before was 
above4  ,let us now stop the ,paper at  
the ,focus ,g1 where the ,light appears 
totally white and circular1 and let us  
consider its whiteness4 ,i say1 that    
this is composed of the converging      
,colours4 ,for if any of those ,colours 

be intercepted at the ,lens1 the        
whiteness will cease and degenerate into
 that ,colour which ariseth from the    
composition of the other ,colours which 
are not intercepted4 ,and then if the   
intercepted ,colours be let pass and    
fall upon that compound ,colour1 they   
mix with it1 and by their mixture       
restore the whiteness4 ,so if the       
violet1 blue and green be intercepted1  
the remaining yellow1 orange and red    
will compound upon the ,paper an orange1
 and then if the intercepted ,colours be
 let pass1 they will fall upon this     
compounded orange1 and together with it 
decompound a white4 ,so also if the red 
and violet be intercepted1 the remaining
 yellow1 green and blue1 will compound a
 green upon the ,paper1 and then the red
 and violet being let pass will fall    
upon this green1 and together with it   
decompound a white4 ,and that in this   
,composition of white the several ,rays 
do not suffer any ,change in their      
colorific ,qualities by acting upon one 

another1 but are only mixed1 and by a   
mixture of their ,colours produce white1
 may farther appear by these ,arguments4
  ,illustration3 ,,fig4 #f4  ,if the    
,paper be placed beyond the ,focus ,g1  
suppose at ,greek3 de1 and then the red 
,colour at the ,lens be alternately     
intercepted1 and let pass again1 the    
violet ,colour on the ,paper will not   
suffer any ,change thereby1 as it ought 
to do if the several sorts of ,rays     
acted upon one another in the ,focus ,g1
 where they cross4 ,neither will the red
 upon the ,paper be changed by any      
alternate stopping1 and letting pass the
 violet which crosseth it4  ,and if the 
,paper be placed at the ,focus ,g1 and  
the white round ,image at ,g be viewed  
through the ,prism ,,hik1 and by the    
,refraction of that ,prism be translated
 to the place rv1 and there appear      
tinged with various ,colours1 namely1   
the violet at v and red at r1 and others
 between1 and then the red ,colours at  
the ,lens be often stopp'd and let pass 

by turns1 the red at r will accordingly 
disappear1 and return as often1 but the 
violet at v will not thereby suffer any 
,change4 ,and so by stopping and letting
 pass alternately the blue at the ,lens1
 the blue at v will accordingly         
disappear and return1 without any       
,change made in the red at r4 ,the red  
therefore depends on one sort of ,rays1 
and the blue on another sort1 which in  
the ,focus ,g where they are commix'd1  
do not act on one another4 ,and there is
 the same ,reason of the other ,colours4
  ,i considered farther1 that when the  
most refrangible ,rays ,pp1 and the     
least refrangible ones ,tt1 are by      
converging inclined to one another1 the 
,paper1 if held very oblique to those   
,rays in the ,focus ,g1 might reflect   
one sort of them more copiously than the
 other sort1 and by that ,means the     
reflected ,light would be tinged in that
 ,focus with the ,colour of the         
predominant ,rays1 provided those ,rays 
severally retained their ,colours1 or   

colorific ,qualities in the ,composition
 of ,white made by them in that ,focus4 
,but if they did not retain them in that
 ,white1 but became all of them         
severally endued there with a           
,disposition to strike the ,sense with  
the ,perception of ,white1 then they    
could never lose their ,whiteness by    
such ,reflexions4 ,i inclined therefore 
the ,paper to the ,rays very obliquely1 
as in the second ,experiment of this    
second ,part of the first ,book1 that   
the most refrangible ,rays1 might be    
more copiously reflected than the rest1 
and the ,whiteness at ,length changed   
successively into blue1 indigo1 and     
violet4 ,then ,i inclined it the        
contrary ,way1 that the least           
refrangible ,rays might be more copious 
in the reflected ,light than the rest1  
and the ,whiteness turned successively  
to yellow1 orange1 and red4  ,lastly1 ,i
 made an ,instrument ,,xy in fashion of 
a ,comb1 whose ,teeth being in number   
sixteen1 were about an ,inch and a half 

broad1 and the ,intervals of the ,teeth 
about two ,inches wide4 ,then by        
interposing successively the ,teeth of  
this ,instrument near the ,lens1 ,i     
intercepted ,part of the ,colours by the
 interposed ,tooth1 whilst the rest of  
them went on through the ,interval of   
the ,teeth to the ,paper ,,de1 and there
 painted a round ,solar ,image4 ,but the
 ,paper ,i had first placed so1 that the
 ,image might appear white as often as  
the ,comb was taken away2 and then the  
,comb being as was said interposed1 that
 ,whiteness by reason of the intercepted
 ,part of the ,colours at the ,lens did 
always change into the ,colour          
compounded of those ,colours which were 
not intercepted1 and that ,colour was by
 the ,motion of the ,comb perpetually   
varied so1 that in the passing of every 
,tooth over the ,lens all these         
,colours1 red1 yellow1 green1 blue1 and 
purple1 did always succeed one another4 
,i caused therefore all the ,teeth to   
pass successively over the ,lens1 and   

when the ,motion was slow1 there        
appeared a perpetual ,succession of the 
,colours upon the ,paper3 ,but if ,i so 
much accelerated the ,motion1 that the  
,colours by reason of their quick       
,succession could not be distinguished  
from one another1 the ,appearance of the
 single ,colours ceased4 ,there was no  
red1 no yellow1 no green1 no blue1 nor  
purple to be seen any longer1 but from a
 ,confusion of them all there arose one 
uniform white ,colour4 ,of the ,light   
which now by the ,mixture of all the    
,colours appeared white1 there was no   
,part really white4 ,one ,part was red1 
another yellow1 a third green1 a fourth 
blue1 a fifth purple1 and every ,part   
retains its proper ,colour till it      
strike the ,sensorium4 ,if the          
,impressions follow one another slowly1 
so that they may be severally perceived1
 there is made a distinct ,sensation of 
all the ,colours one after another in a 
continual ,succession4 ,but if the      
,impressions follow one another so      

quickly1 that they cannot be severally  
perceived1 there ariseth out of them all
 one common ,sensation1 which is neither
 of this ,colour alone nor of that      
alone1 but hath it self indifferently to
 'em all1 and this is a ,sensation of   
,whiteness4 ,by the ,quickness of the   
,successions1 the ,impressions of the   
several ,colours are confounded in the  
,sensorium1 and out of that ,confusion  
ariseth a mix'd ,sensation4 ,if a       
burning ,coal be nimbly moved round in a
 ,circle with ,gyrations continually    
repeated1 the whole ,circle will appear 
like ,fire2 the reason of which is1 that
 the ,sensation of the ,coal in the     
several ,places of that ,circle remains 
impress'd on the ,sensorium1 until the  
,coal return again to the same ,place4  
,and so in a quick ,consecution of the  
,colours the ,impression of every       
,colour remains in the ,sensorium1 until
 a ,revolution of all the ,colours be   
compleated1 and that first ,colour      
return again4 ,the ,impressions         

therefore of all the successive ,colours
 are at once in the ,sensorium1 and     
jointly stir up a ,sensation of them    
all2 and so it is manifest by this      
,experiment1 that the commix'd          
,impressions of all the ,colours do stir
 up and beget a ,sensation of white1    
that is1 that ,whiteness is compounded  
of all the ,colours4  ,and if the ,comb 
be now taken away1 that all the ,colours
 may at once pass from the ,lens to the 
,paper1 and be there intermixed1 and    
together reflected thence to the        
,spectator's ,eyes2 their ,impressions  
on the ,sensorium being now more        
subtilly and perfectly commixed there1  
ought much more to stir up a ,sensation 
of ,whiteness4  ,you may instead of the 
,lens use two ,prisms ,,hik and ,,lmn1  
which by refracting the coloured ,light 
the contrary ,way to that of the first  
,refraction1 may make the diverging     
,rays converge and meet again in ,g1 as 
you see represented in the seventh      
,figure4 ,for where they meet and mix1  

they will compose a white ,light1 as    
when a ,lens is used4  ,exper4 #aa4 ,let
 the ,sun's coloured ,image ,,pt in     
,fig4 #h4 fall upon the ,wall of a dark 
,chamber1 as in the third ,experiment of
 the first ,book1 and let the same be   
viewed through a ,prism abc1 held       
parallel to the ,prism ,,abc1 by whose  
,refraction that ,image was made1 and   
let it now appear lower than before1    
suppose in the ,place ,s over-against   
the red ,colour ,t4 ,and if you go near 
to the ,image ,,pt1 the ,spectrum ,s    
will appear oblong and coloured like the
 ,image ,,pt2 but if you recede from it1
 the ,colours of the spectrum ,s will be
 contracted more and more1 and at length
 vanish1 that ,spectrum ,s becoming     
perfectly round and white2 and if you   
recede yet farther1 the ,colours will   
emerge again1 but in a contrary ,order4 
,now that ,spectrum ,s appears white in 
that ,case1 when the ,rays of several   
sorts which converge from the several   
,parts of the ,image ,,pt1 to the ,prism

 abc1 are so refracted unequally by it1 
that in their ,passage from the ,prism  
to the ,eye they may diverge from one   
and the same ,point of the ,spectrum ,s1
 and so fall afterwards upon one and the
 same ,point in the bottom of the ,eye1 
and there be mingled4  ,illustration3   
,,fig4 #g4  ,illustration3 ,,fig4 #h4   
,and farther1 if the ,comb be here made 
use of1 by whose ,teeth the ,colours at 
the ,image ,,pt may be successively     
intercepted2 the ,spectrum ,s1 when the 
,comb is moved slowly1 will be          
perpetually tinged with successive      
,colours3 ,but when by accelerating the 
,motion of the ,comb1 the ,succession of
 the ,colours is so quick that they     
cannot be severally seen1 that ,spectrum
 ,s1 by a confused and mix'd ,sensation 
of them all1 will appear white4  ,exper4
 #ab4 ,the ,sun shining through a large 
,prism ,,abc in ,fig4 #i4 upon a ,comb  
,,xy1 placed immediately behind the     
,prism1 his ,light which passed through 
the ,interstices of the ,teeth fell upon

 a white ,paper ,,de4 ,the ,breadths of 
the ,teeth were equal to their          
,interstices1 and seven ,teeth together 
with their ,interstices took up an ,inch
 in ,breadth4 ,now1 when the ,paper was 
about two or three ,inches distant from 
the ,comb1 the ,light which passed      
through its several ,interstices painted
 so many ,ranges of ,colours1 kl1 mn1   
op1 qr1 c4 which were parallel to one   
another1 and contiguous1 and without any
 ,mixture of white4 ,and these ,ranges  
of ,colours1 if the ,comb was moved     
continually up and down with a          
reciprocal ,motion1 ascended and        
descended in the ,paper1 and when the   
,motion of the ,comb was so quick1 that 
the ,colours could not be distinguished 
from one another1 the whole ,paper by   
their ,confusion and ,mixture in the    
,sensorium appeared white4              
,illustration3 ,,fig4 #i4  ,let the     
,comb now rest1 and let the ,paper be   
removed farther from the ,prism1 and the
 several ,ranges of ,colours will be    

dilated and expanded into one another   
more and more1 and by mixing their      
,colours will dilute one another1 and at
 length1 when the distance of the ,paper
 from the ,comb is about a ,foot1 or a  
little more 7suppose in the ,place #b;,d
 #b;,e7 they will so far dilute one     
another1 as to become white4  ,with any 
,obstacle1 let all the ,light be now    
stopp'd which passes through any one    
,interval of the ,teeth1 so that the    
,range of ,colours which comes from     
thence may be taken away1 and you will  
see the ,light of the rest of the       
,ranges to be expanded into the ,place  
of the ,range taken away1 and there to  
be coloured4 ,let the intercepted ,range
 pass on as before1 and its ,colours    
falling upon the ,colours of the other  
,ranges1 and mixing with them1 will     
restore the ,whiteness4  ,let the ,paper
 #b;,d #b;,e be now very much inclined  
to the ,rays1 so that the most          
refrangible ,rays may be more copiously 
reflected than the rest1 and the white  

,colour of the ,paper through the       
,excess of those ,rays will be changed  
into blue and violet4 ,let the ,paper be
 as much inclined the contrary way1 that
 the least refrangible ,rays may be now 
more copiously reflected than the rest1 
and by their ,excess the ,whiteness will
 be changed into yellow and red4 ,the   
several ,rays therefore in that white   
,light do retain their colorific        
,qualities1 by which those of any sort1 
whenever they become more copious than  
the rest1 do by their ,excess and       
,predominance cause their proper ,colour
 to appear4  ,and by the same way of    
arguing1 applied to the third           
,experiment of this second ,part of the 
first ,book1 it may be concluded1 that  
the white ,colour of all refracted      
,light at its very first ,emergence1    
where it appears as white as before its 
,incidence1 is compounded of various    
,colours4  ,illustration3 ,,fig4 #aj4   
,exper4 #ac4 ,in the foregoing          
,experiment the several ,intervals of   

the ,teeth of the ,comb do the ,office  
of so many ,prisms1 every ,interval     
producing the ,phaenomenon of one       
,prism4 ,whence instead of those        
,intervals using several ,prisms1 ,i    
try'd to compound ,whiteness by mixing  
their ,colours1 and did it by using only
 three ,prisms1 as also by using only   
two as follows4 ,let two ,prisms ,,abc  
and abc1 in ,fig4 #aj4 whose refracting 
,angles ,b and b are equal1 be so placed
 parallel to one another1 that the      
refracting ,angle ,b of the one may     
touch the ,angle c at the ,base of the  
other1 and their ,planes ,,cb and cb1 at
 which the ,rays emerge1 may lie in     
,directum4 ,then let the ,light         
trajected through them fall upon the    
,paper ,,mn1 distant about #h or #ab    
,inches from the ,prisms4 ,and the      
,colours generated by the interior      
,limits ,b and c of the two ,prisms1    
will be mingled at ,,pt1 and there      
compound white4 ,for if either ,prism be
 taken away1 the ,colours made by the   

other will appear in that ,place ,,pt1  
and when the ,prism is restored to its  
,place again1 so that its ,colours may  
there fall upon the ,colours of the     
other1 the ,mixture of them both will   
restore the ,whiteness4  ,this          
,experiment succeeds also1 as ,i have   
tried1 when the ,angle b of the lower   
,prism1 is a little greater than the    
,angle ,b of the upper1 and between the 
interior ,angles ,b and c1 there        
intercedes some ,space ,bc1 as is       
represented in the ,figure1 and the     
refracting ,planes ,,bc and bc1 are     
neither in ,directum1 nor parallel to   
one another4 ,for there is nothing more 
requisite to the ,success of this       
,experiment1 than that the ,rays of all 
sorts may be uniformly mixed upon the   
,paper in the ,place ,,pt4 ,if the most 
refrangible ,rays coming from the       
superior ,prism take up all the ,space  
from ,m to ,p1 the ,rays of the same    
sort which come from the inferior ,prism
 ought to begin at ,p1 and take up all  

the rest of the ,space from thence      
towards ,n4 ,if the least refrangible   
,rays coming from the superior ,prism   
take up the ,space ,,mt1 the ,rays of   
the same kind which come from the other 
,prism ought to begin at ,t1 and take up
 the remaining ,space ,,tn4 ,if one sort
 of the ,rays which have intermediate   
,degrees of ,refrangibility1 and come   
from the superior ,prism be extended    
through the ,space ,,mq1 and another    
sort of those ,rays through the ,space  
,,mr1 and a third sort of them through  
the ,space ,,ms1 the same sorts of ,rays
 coming from the lower ,prism1 ought to 
illuminate the remaining ,spaces ,,qn1  
,,rn1 ,,sn1 respectively4 ,and the same 
is to be understood of all the other    
sorts of ,rays4 ,for thus the ,rays of  
every sort will be scattered uniformly  
and evenly through the whole ,space     
,,mn1 and so being every where mix'd in 
the same ,proportion1 they must every   
where produce the same ,colour4 ,and    
therefore1 since by this ,mixture they  

produce white in the ,exterior ,spaces  
,,mp and ,,tn1 they must also produce   
white in the ,interior ,space ,,pt4     
,this is the reason of the ,composition 
by which ,whiteness was produced in this
 ,experiment1 and by what other way     
soever ,i made the like ,composition1   
the ,result was ,whiteness4  ,lastly1   
,if with the ,teeth of a ,comb of a due 
,size1 the coloured ,lights of the two  
,prisms which fall upon the ,space ,,pt 
be alternately intercepted1 that ,space 
,,pt1 when the ,motion of the ,comb is  
slow1 will always appear coloured1 but  
by accelerating the ,motion of the ,comb
 so much that the successive ,colours   
cannot be distinguished from one        
another1 it will appear white4  ,exper4 
#ad4 ,hitherto ,i have produced         
,whiteness by mixing the ,colours of    
,prisms4 ,if now the ,colours of natural
 ,bodies are to be mingled1 let ,water a
 little thicken'd with ,soap be agitated
 to raise a ,froth1 and after that      
,froth has stood a little1 there will   

appear to one that shall view it        
intently various ,colours every where in
 the ,surfaces of the several ,bubbles2 
but to one that shall go so far off1    
that he cannot distinguish the ,colours 
from one another1 the whole ,froth will 
grow white with a perfect ,whiteness4   
,exper4 #ae4 ,lastly1 ,in attempting to 
compound a white1 by mixing the coloured
 ,powders which ,painters use1 ,i       
consider'd that all colour'd ,powders do
 suppress and stop in them a very       
considerable ,part of the ,light by     
which they are illuminated4 ,for they   
become colour'd by reflecting the ,light
 of their own ,colours more copiously1  
and that of all other ,colours more     
sparingly1 and yet they do not reflect  
the ,light of their own ,colours so     
copiously as white ,bodies do4 ,if red  
,lead1 for instance1 and a white ,paper1
 be placed in the red ,light of the     
colour'd ,spectrum made in a dark       
,chamber by the ,refraction of a ,prism1
 as is described in the third           

,experiment of the first ,part of this  
,book2 the ,paper will appear more lucid
 than the red ,lead1 and therefore      
reflects the red-making ,rays more      
copiously than red ,lead doth4 ,and if  
they be held in the ,light of any other 
,colour1 the ,light reflected by the    
,paper will exceed the ,light reflected 
by the red ,lead in a much greater      
,proportion4 ,and the like happens in   
,powders of other ,colours4 ,and        
therefore by mixing such ,powders1 we   
are not to expect a strong and full     
,white1 such as is that of ,paper1 but  
some dusky obscure one1 such as might   
arise from a ,mixture of ,light and     
,darkness1 or from white and black1 that
 is1 a grey1 or dun1 or russet brown1   
such as are the ,colours of a ,man's    
,nail1 of a ,mouse1 of ,ashes1 of       
ordinary ,stones1 of ,mortar1 of ,dust  
and ,dirt in ,high-ways1 and the like4  
,and such a dark white ,i have often    
produced by mixing colour'd ,powders4   
,for thus one ,part of red ,lead1 and   

five ,parts of ,viride ,a,eris1 composed
 a dun ,colour like that of a ,mouse4   
,for these two ,colours were severally  
so compounded of others1 that in both   
together were a ,mixture of all         
,colours2 and there was less red ,lead  
used than ,viride ,a,eris1 because of   
the ,fulness of its ,colour4 ,again1 one
 ,part of red ,lead1 and four ,parts of 
blue ,bise1 composed a dun ,colour      
verging a little to purple1 and by      
adding to this a certain ,mixture of    
,orpiment and ,viride ,a,eris in a due  
,proportion1 the ,mixture lost its      
purple ,tincture1 and became perfectly  
dun4 ,but the ,experiment succeeded best
 without ,minium thus4 ,to ,orpiment ,i 
added by little and little a certain    
full bright purple1 which ,painters use1
 until the ,orpiment ceased to be       
yellow1 and became of a pale red4 ,then 
,i diluted that red by adding a little  
,viride ,a,eris1 and a little more blue 
,bise than ,viride ,a,eris1 until it    
became of such a grey or pale white1 as 

verged to no one of the ,colours more   
than to another4 ,for thus it became of 
a ,colour equal in ,whiteness to that of
 ,ashes1 or of ,wood newly cut1 or of a 
,man's ,skin4 ,the ,orpiment reflected  
more ,light than did any other of the   
,powders1 and therefore conduced more to
 the ,whiteness of the compounded       
,colour than they4 ,to assign the       
,proportions accurately may be          
difficult1 by reason of the different   
,goodness of ,powders of the same kind4 
,accordingly1 as the ,colour of any     
,powder is more or less full and        
luminous1 it ought to be used in a less 
or greater ,proportion4  ,now1          
considering that these grey and dun     
,colours may be also produced by mixing 
,whites and ,blacks1 and by consequence 
differ from perfect ,whites1 not in     
,species of ,colours1 but only in degree
 of ,luminousness1 it is manifest that  
there is nothing more requisite to make 
them perfectly white than to increase   
their ,light sufficiently2 and1 on the  

contrary1 if by increasing their ,light 
they can be brought to perfect          
,whiteness1 it will thence also follow1 
that they are of the same ,species of   
,colour with the best ,whites1 and      
differ from them only in the ,quantity  
of ,light4 ,and this ,i tried as        
follows4 ,i took the third of the       
above-mention'd grey ,mixtures1 7that   
which was compounded of ,orpiment1      
,purple1 ,bise1 and ,viride ,a,eris7 and
 rubbed it thickly upon the ,floor of my
 ,chamber1 where the ,sun shone upon it 
through the opened ,casement2 and by it1
 in the shadow1 ,i laid a ,piece of     
white ,paper of the same ,bigness4 ,then
 going from them to the distance of #ab 
or #ah ,feet1 so that ,i could not      
discern the ,unevenness of the ,surface 
of the ,powder1 nor the little ,shadows 
let fall from the gritty ,particles     
thereof2 the ,powder appeared intensely 
white1 so as to transcend even the      
,paper it self in ,whiteness1 especially
 if the ,paper were a little shaded from

 the ,light of the ,clouds1 and then the
 ,paper compared with the ,powder       
appeared of such a grey ,colour as the  
,powder had done before4 ,but by laying 
the ,paper where the ,sun shines through
 the ,glass of the ,window1 or by       
shutting the ,window that the ,sun might
 shine through the ,glass upon the      
,powder1 and by such other fit ,means of
 increasing or decreasing the ,lights   
wherewith the ,powder and ,paper were   
illuminated1 the ,light wherewith the   
,powder is illuminated may be made      
stronger in such a due ,proportion than 
the ,light wherewith the ,paper is      
illuminated1 that they shall both appear
 exactly alike in ,whiteness4 ,for when 
,i was trying this1 a ,friend coming to 
visit me1 ,i stopp'd him at the ,door1  
and before ,i told him what the ,colours
 were1 or what ,i was doing2 ,i asked   
him1 ,which of the two ,whites were the 
best1 and wherein they differed8 ,and   
after he had at that distance viewed    
them well1 he answer'd1 that they were  

both good ,whites1 and that he could not
 say which was best1 nor wherein their  
,colours differed4 ,now1 if you         
consider1 that this ,white of the       
,powder in the ,sun-shine was compounded
 of the ,colours which the component    
,powders 7,orpiment1 ,purple1 ,bise1 and
 ,viride ,a,eris7 have in the same      
,sun-shine1 you must acknowledge by this
 ,experiment1 as well as by the former1 
that perfect ,whiteness may be          
compounded of ,colours4  ,from what has 
been said it is also evident1 that the  
,whiteness of the ,sun's ,light is      
compounded of all the ,colours wherewith
 the several sorts of ,rays whereof that
 ,light consists1 when by their several 
,refrangibilities they are separated    
from one another1 do tinge ,paper or any
 other white ,body whereon they fall4   
,for those ,colours 7by ,prop4 ,,ii4    
,part #b47 are unchangeable1 and        
whenever all those ,rays with those     
their ,colours are mix'd again1 they    
reproduce the same white ,light as      

before4   ,,prop4 ,,vi4 ,,prob4 ,,ii4   
,in a mixture of ,primary ,colours1 the 
,quantity and ,quality of each being    
given1 to know the ,colour of the       
,compound4  ,illustration3 ,,fig4 #aa4  
,with the ,center ,o in ,fig4 #aa4 and  
,radius ,,od describe a ,circle ,,adf1  
and distinguish its ,circumference into 
seven ,parts ,,de1 ,,ef1 ,,fg1 ,,ga1    
,,ab1 ,,bc1 ,,cd1 proportional to the   
seven ,musical ,tones or ,intervals of  
the eight ,sounds1 ,sol1 la1 fa1 sol1   
la1 mi1 fa1 sol1 contained in an eight1 
that is1 proportional to the ,number    
#a_/i1 #a_/af1 #a_/aj1 #a_/i1 #a_/af1   
#a_/af1 #a_/i4 ,let the first ,part ,,de
 represent a red ,colour1 the second    
,,ef orange1 the third ,,fg yellow1 the 
fourth ,,ca green1 the fifth ,,ab blue1 
the sixth ,,bc indigo1 and the seventh  
,,cd violet4 ,and conceive that these   
are all the ,colours of uncompounded    
,light gradually passing into one       
another1 as they do when made by        
,prisms2 the ,circumference ,,defgabcd1 

representing the whole ,series of       
,colours from one end of the ,sun's     
colour'd ,image to the other1 so that   
from ,d to ,e be all degrees of red1 at 
,e the mean ,colour between red and     
orange1 from ,e to ,f all degrees of    
orange1 at ,f the mean between orange   
and yellow1 from ,f to ,g all degrees of
 yellow1 and so on4 ,let p be the       
,center of ,gravity of the ,arch ,,de1  
and q1 r1 s1 t1 u1 x1 the ,centers of   
,gravity of the ,arches ,,ef1 ,,fg1     
,,ga1 ,,ab1 ,,bc1 and ,,cd respectively1
 and about those ,centers of ,gravity   
let ,circles proportional to the ,number
 of ,rays of each ,colour in the given  
,mixture be describ'd3 that is1 the     
,circle p proportional to the ,number of
 the red-making ,rays in the ,mixture1  
the ,circle q proportional to the       
,number of the orange-making ,rays in   
the ,mixture1 and so of the rest4 ,find 
the common ,center of ,gravity of all   
those ,circles1 p1 q1 r1 s1 t1 u1 x4    
,let that ,center be ,z2 and from the   

,center of the ,circle ,,adf1 through ,z
 to the ,circumference1 drawing the     
,right ,line ,,oy1 the ,place of the    
,point ,y in the ,circumference shall   
shew the ,colour arising from the       
,composition of all the ,colours in the 
given ,mixture1 and the ,line ,,oz shall
 be proportional to the ,fulness or     
,intenseness of the ,colour1 that is1 to
 its distance from ,whiteness4 ,as if ,y
 fall in the middle between ,f and ,g1  
the compounded ,colour shall be the best
 yellow2 if ,y verge from the middle    
towards ,f or ,g1 the compound ,colour  
shall accordingly be a yellow1 verging  
towards orange or green4 ,if ,z fall    
upon the ,circumference1 the ,colour    
shall be intense and florid in the      
highest ,degree2 if it fall in the      
mid-way between the ,circumference and  
,center1 it shall be but half so        
intense1 that is1 it shall be such a    
,colour as would be made by diluting the
 intensest yellow with an equal quantity
 of whiteness2 and if it fall upon the  

center ,o1 the ,colour shall have lost  
all its intenseness1 and become a white4
 ,but it is to be noted1 ,that if the   
point ,z fall in or near the line ,,od1 
the main ingredients being the red and  
violet1 the ,colour compounded shall not
 be any of the prismatick ,colours1 but 
a purple1 inclining to red or violet1   
accordingly as the point ,z lieth on the
 side of the line ,,do towards ,e or    
towards ,c1 and in general the          
compounded violet is more bright and    
more fiery than the uncompounded4 ,also 
if only two of the primary ,colours     
which in the circle are opposite to one 
another be mixed in an equal proportion1
 the point ,z shall fall upon the center
 ,o1 and yet the ,colour compounded of  
those two shall not be perfectly white1 
but some faint anonymous ,colour4 ,for  
,i could never yet by mixing only two   
primary ,colours produce a perfect      
white4 ,whether it may be compounded of 
a mixture of three taken at equal       
distances in the circumference ,i do not

 know1 but of four or five ,i do not    
much question but it may4 ,but these are
 ,curiosities of little or no moment to 
the understanding the ,phaenomena of    
,nature4 ,for in all whites produced by 
,nature1 there uses to be a mixture of  
all sorts of ,rays1 and by consequence a
 composition of all ,colours4  ,to give 
an instance of this ,rule2 suppose a    
,colour is compounded of these          
homogeneal ,colours1 of violet one part1
 of indigo one part1 of blue two parts1 
of green three parts1 of yellow five    
parts1 of orange six parts1 and of red  
ten parts4 ,proportional to these parts 
describe the ,circles x1 v1 t1 s1 r1 q1 
p1 respectively1 that is1 so that if the
 ,circle x be one1 the ,circle v may be 
one1 the ,circle t two1 the ,circle s   
three1 and the ,circles r1 q and p1     
five1 six and ten4 ,then ,i find ,z the 
common center of gravity of these       
,circles1 and through ,z drawing the    
,line ,,oy1 the ,point ,y falls upon the
 circumference between ,e and ,f1       

something nearer to ,e than to ,f1 and  
thence ,i conclude1 that the ,colour    
compounded of these ,ingredients will be
 an orange1 verging a little more to red
 than to yellow4 ,also ,i find that ,,oz
 is a little less than one half of ,,oy1
 and thence ,i conclude1 that this      
orange hath a little less than half the 
fulness or intenseness of an            
uncompounded orange2 that is to say1    
that it is such an orange as may be made
 by mixing an homogeneal orange with a  
good white in the proportion of the     
,line ,,oz to the ,line ,,zy1 this      
,proportion being not of the quantities 
of mixed orange and white ,powders1 but 
of the quantities of the ,lights        
reflected from them4  ,this ,rule ,i    
conceive accurate enough for practice1  
though not mathematically accurate2 and 
the truth of it may be sufficiently     
proved to ,sense1 by stopping any of the
 ,colours at the ,lens in the tenth     
,experiment of this ,book4 ,for the rest
 of the ,colours which are not stopp'd1 

but pass on to the ,focus of the ,lens1 
will there compound either accurately or
 very nearly such a ,colour1 as by this 
,rule ought to result from their        
,mixture4   ,,prop4 ,,vii4 ,,theor4 ,v4 
,all the ,colours in the ,universe which
 are made by ,light1 and depend not on  
the ,power of ,imagination1 are either  
the ,colours of homogeneal ,lights1 or  
compounded of these1 and that either    
accurately or very nearly1 according to 
the ,rule of the foregoing ,problem4    
,for it has been proved 7in ,prop4 #a4  
,part #b47 that the changes of ,colours 
made by ,refractions do not arise from  
any new ,modifications of the ,rays     
impress'd by those ,refractions1 and by 
the various ,terminations of ,light and 
,shadow1 as has been the constant and   
general ,opinion of ,philosophers4 ,it  
has also been proved that the several   
,colours of the homogeneal ,rays do     
constantly answer to their degrees of   
,refrangibility1 7,prop4 #a4 ,part #a4  
and ,prop4 #b4 ,part #b47 and that their

 degrees of ,refrangibility cannot be   
changed by ,refractions and ,reflexions 
7,prop4 #b4 ,part #a47 and by           
consequence that those their ,colours   
are likewise immutable4 ,it has also    
been proved directly by refracting and  
reflecting homogeneal ,lights apart1    
that their ,colours cannot be changed1  
7,prop4 #b4 ,part #b47 ,it has been     
proved also1 that when the several sorts
 of ,rays are mixed1 and in crossing    
pass through the same space1 they do not
 act on one another so as to change each
 others colorific qualities4 7,exper4   
#aj4 ,part #b47 but by mixing their     
,actions in the ,sensorium beget a      
,sensation differing from what either   
would do apart1 that is a ,sensation of 
a mean ,colour between their proper     
,colours2 and particularly when by the  
concourse and mixtures of all sorts of  
,rays1 a white ,colour is produced1 the 
white is a mixture of all the ,colours  
which the ,rays would have apart1       
7,prop4 #e4 ,part #b47 ,the ,rays in    

that mixture do not lose or alter their 
several colorific qualities1 but by all 
their various kinds of ,actions mix'd in
 the ,sensorium1 beget a ,sensation of a
 middling ,colour between all their     
,colours1 which is whiteness4 ,for      
whiteness is a mean between all         
,colours1 having it self indifferently  
to them all1 so as with equal facility  
to be tinged with any of them4 ,a red   
,powder mixed with a little blue1 or a  
blue with a little red1 doth not        
presently lose its ,colour1 but a white 
,powder mix'd with any ,colour is       
presently tinged with that ,colour1 and 
is equally capable of being tinged with 
any ,colour whatever4 ,it has been      
shewed also1 that as the ,sun's ,light  
is mix'd of all sorts of ,rays1 so its  
whiteness is a mixture of the ,colours  
of all sorts of ,rays2 those ,rays      
having from the beginning their several 
colorific qualities as well as their    
several ,refrangibilities1 and retaining
 them perpetually unchanged             

notwithstanding any ,refractions or     
,reflexions they may at any time suffer1
 and that whenever any sort of the      
,sun's ,rays is by any means 7as by     
,reflexion in ,exper4 #i1 and #aj4 ,part
 #a4 or by ,refraction as happens in all
 ,refractions7 separated from the rest1 
they then manifest their proper         
,colours4 ,these things have been       
prov'd1 and the sum of all this amounts 
to the ,proposition here to be proved4  
,for if the ,sun's ,light is mix'd of   
several sorts of ,rays1 each of which   
have originally their several           
,refrangibilities and colorific         
,qualities1 and notwithstanding their   
,refractions and ,reflexions1 and their 
various ,separations or ,mixtures1 keep 
those their original ,properties        
perpetually the same without alteration2
 then all the ,colours in the ,world    
must be such as constantly ought to     
arise from the original colorific       
qualities of the ,rays whereof the      
,lights consist by which those ,colours 

are seen4 ,and therefore if the reason  
of any ,colour whatever be required1 we 
have nothing else to do than to consider
 how the ,rays in the ,sun's ,light have
 by ,reflexions or ,refractions1 or     
other causes1 been parted from one      
another1 or mixed together2 or otherwise
 to find out what sorts of ,rays are in 
the ,light by which that ,colour is     
made1 and in what ,proportion2 and then 
by the last ,problem to learn the       
,colour which ought to arise by mixing  
those ,rays 7or their ,colours7 in that 
proportion4 ,i speak here of ,colours so
 far as they arise from ,light4 ,for    
they appear sometimes by other ,causes1 
as when by the power of ,phantasy we see
 ,colours in a ,dream1 or a ,mad-man    
sees things before him which are not    
there2 or when we see ,fire by striking 
the ,eye1 or see ,colours like the ,eye 
of a ,peacock's ,feather1 by pressing   
our ,eyes in either corner whilst we    
look the other way4 ,where these and    
such like ,causes interpose not1 the    

,colour always answers to the sort or   
sorts of the ,rays whereof the ,light   
consists1 as ,i have constantly found in
 whatever ,phaenomena of ,colours ,i    
have hitherto been able to examine4 ,i  
shall in the following ,propositions    
give instances of this in the           
,phaenomena of chiefest note4   ,,prop4 
,,viii4 ,,prob4 ,,iii4  ,by the         
discovered ,properties of ,light to     
explain the ,colours made by ,prisms4   
,let ,,abc in ,fig4 #ab4 represent a    
,prism refracting the ,light of the     
,sun1 which comes into a dark ,chamber  
through a hole ,f,greek3 ph almost as   
broad as the ,prism1 and let ,,mn       
represent a white ,paper on which the   
refracted ,light is cast1 and suppose   
the most refrangible or deepest         
violet-making ,rays fall upon the ,space
 ,p,greek3 p1 the least refrangible or  
deepest red-making ,rays upon the ,space
 ,t,greek3 t1 the middle sort between   
the indigo-making and blue-making ,rays 
upon the ,space ,q,greek3 ch1 the middle

 sort of the green-making ,rays upon the
 ,space ,r1 the middle sort between the 
yellow-making and orange-making ,rays   
upon the ,space ,s,greek3 s1 and other  
intermediate sorts upon intermediate    
,spaces4 ,for so the ,spaces upon which 
the several sorts adequately fall will  
by reason of the different              
,refrangibility of those sorts be one   
lower than another4 ,now if the ,paper  
,,mn be so near the ,prism that the     
,spaces ,,pt and ,greek3 pt do not      
interfere with one another1 the distance
 between them ,t,greek3 p will be       
illuminated by all the sorts of ,rays in
 that proportion to one another which   
they have at their very first coming out
 of the ,prism1 and consequently be     
white4 ,but the ,spaces ,,pt and ,greek3
 pt on either hand1 will not be         
illuminated by them all1 and therefore  
will appear coloured4 ,and particularly 
at ,p1 where the outmost violet-making  
,rays fall alone1 the ,colour must be   
the deepest violet4 ,at ,q where the    

violet-making and indigo-making ,rays   
are mixed1 it must be a violet inclining
 much to indigo4 ,at ,r where the       
violet-making1 indigo-making1           
blue-making1 and one half of the        
green-making ,rays are mixed1 their     
,colours must 7by the construction of   
the second ,problem7 compound a middle  
,colour between indigo and blue4 ,at ,s 
where all the ,rays are mixed1 except   
the red-making and orange-making1 their 
,colours ought by the same ,rule to     
compound a faint blue1 verging more to  
green than indigo4 ,and in the progress 
from ,s to ,t1 this blue will grow more 
and more faint and dilute1 till at ,t1  
where all the ,colours begin to be      
mixed1 it ends in whiteness4            
,illustration3 ,,fig4 #ab4  ,so again1  
on the other side of the white at       
,greek3 t1 where the least refrangible  
or utmost red-making ,rays are alone1   
the ,colour must be the deepest red4 ,at
 ,greek3 s the mixture of red and orange
 will compound a red inclining to       

orange4 ,at ,greek3 r the mixture of    
red1 orange1 yellow1 and one half of the
 green must compound a middle ,colour   
between orange and yellow4 ,at ,greek3  
ch the mixture of all ,colours but      
violet and indigo will compound a faint 
yellow1 verging more to green than to   
orange4 ,and this yellow will grow more 
faint and dilute continually in its     
progress from ,greek3 ch to ,greek3 p1  
where by a mixture of all sorts of ,rays
 it will become white4  ,these ,colours 
ought to appear were the ,sun's ,light  
perfectly white3 ,but because it        
inclines to yellow1 the ,excess of the  
yellow-making ,rays whereby 'tis tinged 
with that ,colour1 being mixed with the 
faint blue between ,s and ,t1 will draw 
it to a faint green4 ,and so the        
,colours in order from ,p to ,greek3 t  
ought to be violet1 indigo1 blue1 very  
faint green1 white1 faint yellow1       
orange1 red4 ,thus it is by the         
computation3 ,and they that please to   
view the ,colours made by a ,prism will 

find it so in ,nature4  ,these are the  
,colours on both sides the white when   
the ,paper is held between the ,prism   
and the ,point ,x where the ,colours    
meet1 and the interjacent white         
vanishes4 ,for if the ,paper be held    
still farther off from the ,prism1 the  
most refrangible and least refrangible  
,rays will be wanting in the middle of  
the ,light1 and the rest of the ,rays   
which are found there1 will by mixture  
produce a fuller green than before4     
,also the yellow and blue will now      
become less compounded1 and by          
consequence more intense than before4   
,and this also agrees with experience4  
,and if one look through a ,prism upon a
 white ,object encompassed with         
blackness or darkness1 the reason of the
 ,colours arising on the edges is much  
the same1 as will appear to one that    
shall a little consider it4 ,if a black 
,object be encompassed with a white one1
 the ,colours which appear through the  
,prism are to be derived from the ,light

 of the white one1 spreading into the   
,regions of the black1 and therefore    
they appear in a contrary order to that1
 when a white ,object is surrounded with
 black4 ,and the same is to be          
understood when an ,object is viewed1   
whose parts are some of them less       
luminous than others4 ,for in the       
borders of the more and less luminous   
,parts1 ,colours ought always by the    
same ,principles to arise from the      
,excess of the ,light of the more       
luminous1 and to be of the same kind as 
if the darker parts were black1 but yet 
to be more faint and dilute4  ,what is  
said of ,colours made by ,prisms may be 
easily applied to ,colours made by the  
,glasses of ,telescopes or ,microscopes1
 or by the ,humours of the ,eye4 ,for if
 the ,object-glass of a ,telescope be   
thicker on one side than on the other1  
or if one half of the ,glass1 or one    
half of the ,pupil of the ,eye be       
cover'd with any opake substance2 the   
,object-glass1 or that part of it or of 

the ,eye which is not cover'd1 may be   
consider'd as a ,wedge with crooked     
,sides1 and every ,wedge of ,glass or   
other pellucid ,substance has the effect
 of a ,prism in refracting the ,light   
which passes through it4,l  ,how the    
,colours in the ninth and tenth         
,experiments of the first ,part arise   
from the different ,reflexibility of    
,light1 is evident by what was there    
said4 ,but it is observable in the ninth
 ,experiment1 that whilst the ,sun's    
direct ,light is yellow1 the ,excess of 
the blue-making ,rays in the reflected  
beam of ,light ,,mn1 suffices only to   
bring that yellow to a pale white       
inclining to blue1 and not to tinge it  
with a manifestly blue ,colour4 ,to     
obtain therefore a better blue1 ,i used 
instead of the yellow ,light of the ,sun
 the white ,light of the ,clouds1 by    
varying a little the ,experiment1 as    
follows4  ,illustration3 ,,fig4 #ac4    
,exper4 #af ,let ,,hfg in ,fig4 #ac4    
represent a ,prism in the open ,air1 and

 ,s the ,eye of the ,spectator1 viewing 
the ,clouds by their ,light coming into 
the ,prism at the ,plane ,side ,,figk1  
and reflected in it by its ,base ,,heig1
 and thence going out through its ,plane
 ,side ,,hefk to the ,eye4 ,and when the
 ,prism and ,eye are conveniently       
placed1 so that the ,angles of          
,incidence and ,reflexion at the ,base  
may be about #dj ,degrees1 the          
,spectator will see a ,bow ,,mn of a    
blue ,colour1 running from one ,end of  
the ,base to the other1 with the        
,concave ,side towards him1 and the     
,part of the ,base ,,imng beyond this   
,bow will be brighter than the other    
,part ,,emnh on the other ,side of it4  
,this blue ,colour ,,mn being made by   
nothing else than by ,reflexion of a    
specular ,superficies1 seems so odd a   
,phaenomenon1 and so difficult to be    
explained by the vulgar ,hypothesis of  
,philosophers1 that ,i could not but    
think it deserved to be taken ,notice   
of4 ,now for understanding the ,reason  

of it1 suppose the ,plane ,,abc to cut  
the ,plane ,sides and ,base of the      
,prism perpendicularly4 ,from the ,eye  
to the ,line ,,bc1 wherein that ,plane  
cuts the ,base1 draw the ,lines ,sp and 
,st1 in the ,angles ,spc #ej degr4      
#a_/i1 and ,stc #di degr4 #a_/bh1 and   
the ,point p will be the ,limit beyond  
which none of the most refrangible ,rays
 can pass through the ,base of the      
,prism1 and be refracted1 whose         
,incidence is such that they may be     
reflected to the ,eye2 and the ,point t 
will be the like ,limit for the least   
refrangible ,rays1 that is1 beyond which
 none of them can pass through the      
,base1 whose ,incidence is such that by 
,reflexion they may come to the ,eye4   
,and the ,point r taken in the middle   
,way between p and t1 will be the like  
,limit for the meanly refrangible ,rays4
 ,and therefore all the least           
refrangible ,rays which fall upon the   
,base beyond t1 that is1 between t and  
,b1 and can come from thence to the     

,eye1 will be reflected thither3 ,but on
 this side t1 that is1 between t and c1 
many of these ,rays will be transmitted 
through the ,base4 ,and all the most    
refrangible ,rays which fall upon the   
,base beyond p1 that is1 between1 p and 
,b1 and can by ,reflexion come from     
thence to the ,eye1 will be reflected   
thither1 but every where between p and  
c1 many of these ,rays will get through 
the ,base1 and be refracted2 and the    
same is to be understood of the meanly  
refrangible ,rays on either side of the 
,point r4 ,whence it follows1 that the  
,base of the ,prism must every where    
between t and ,b1 by a total ,reflexion 
of all sorts of ,rays to the ,eye1 look 
white and bright4 ,and every where      
between p and ,c1 by reason of the      
,transmission of many ,rays of every    
sort1 look more pale1 obscure1 and dark4
 ,but at r1 and in other ,places between
 p and t1 where all the more refrangible
 ,rays are reflected to the ,eye1 and   
many of the less refrangible are        

transmitted1 the ,excess of the most    
refrangible in the reflected ,light will
 tinge that ,light with their ,colour1  
which is violet and blue4 ,and this     
happens by taking the ,line ,c prt ,b   
any where between the ,ends of the      
,prism ,,hg and ,,ei4   ,,prop4 ,,ix4   
,,prob4 ,,iv4  ,by the discovered       
,properties of ,light to explain the    
,colours of the ,rain-bow4              
,illustration3 ,,fig4 #ad4  ,this ,bow  
never appears1 but where it rains in the
 ,sun-shine1 and may be made            
artificially by spouting up ,water which
 may break aloft1 and scatter into      
,drops1 and fall down like ,rain4 ,for  
the ,sun shining upon these ,drops      
certainly causes the ,bow to appear to a
 ,spectator standing in a due ,position 
to the ,rain and ,sun4 ,and hence it is 
now agreed upon1 that this ,bow is made 
by ,refraction of the ,sun's ,light in  
drops of falling ,rain4 ,this was       
understood by some of the ,antients1 and
 of late more fully discover'd and      

explain'd by the famous ,antonius de    
,dominis ,archbishop of ,spalato1 in his
 book ,de ,radiis ,visus  ,lucis1       
published by his ,friend ,bartolus at   
,venice1 in the ,year #afaa1 and written
 above #bj ,years before4 ,for he       
teaches there how the interior ,bow is  
made in round ,drops of ,rain by two    
,refractions of the ,sun's ,light1 and  
one ,reflexion between them1 and the    
exterior by two ,refractions1 and two   
sorts of ,reflexions between them in    
each ,drop of ,water1 and proves his    
,explications by ,experiments made with 
a ,phial full of ,water1 and with       
,globes of ,glass filled with ,water1   
and placed in the ,sun to make the      
,colours of the two ,bows appear in     
them4 ,the same ,explication            
,des-,cartes hath pursued in his        
,meteors1 and mended that of the        
exterior ,bow4 ,but whilst they         
understood not the true ,origin of      
,colours1 it's necessary to pursue it   
here a little farther4 ,for             

understanding therefore how the ,bow is 
made1 let a ,drop of ,rain1 or any other
 spherical transparent ,body be         
represented by the ,sphere ,,bnfg1 in   
,fig4 #ad4 described with the ,center   
,c1 and ,semi-diameter ,,cn4 ,and let   
,,an be one of the ,sun's ,rays incident
 upon it at ,n1 and thence refracted to 
,f1 where let it either go out of the   
,sphere by ,refraction towards ,v1 or be
 reflected to ,g2 and at ,g let it      
either go out by ,refraction to ,r1 or  
be reflected to ,h2 and at ,h let it go 
out by ,refraction towards ,s1 cutting  
the incident ,ray in ,y4 ,produce ,,an  
and ,,rg1 till they meet in ,x1 and upon
 ,,ax and ,,nf1 let fall the            
,perpendiculars ,,cd and ,,ce1 and      
produce ,,cd till it fall upon the      
,circumference at ,l4 ,parallel to the  
incident ,ray ,,an draw the ,diameter   
,,bq1 and let the ,sine of ,incidence   
out of ,air into ,water be to the ,sine 
of ,refraction as ,i to ,r4 ,now1 if you
 suppose the ,point of ,incidence ,n to 

move from the ,point ,b1 continually    
till it come to ,l1 the ,arch ,,qf will 
first increase and then decrease1 and so
 will the ,angle ,,axr which the ,rays  
,,an and ,,gr contain2 and the ,arch    
,,qf and ,angle ,,axr will be biggest   
when ,,nd is to ,,cn as sqrt7,,ii -     
,,rr7 to sqrt7#c7,,rr1 in which case    
,,ne will be to ,,nd as #b,r to ,i4     
,also the ,angle ,,ays1 which the ,rays 
,,an and ,,hs contain will first        
decrease1 and then increase and grow    
least when ,,nd is to ,,cn as sqrt7,,ii 
- ,,rr7 to sqrt7#h7,,rr1 in which case  
,,ne will be to ,,nd1 as #c,r to ,i4    
,and so the ,angle which the next       
emergent ,ray 7that is1 the emergent    
,ray after three ,reflexions7 contains  
with the incident ,ray ,,an will come to
 its ,limit when ,,nd is to ,,cn as     
sqrt7,,ii - ,,rr7 to sqrt7#ae7,,rr1 in  
which case ,,ne will be to ,,nd as #d,r 
to ,i4 ,and the ,angle which the ,ray   
next after that ,emergent1 that is1 the 
,ray emergent after four ,reflexions1   

contains with the ,incident1 will come  
to its ,limit1 when ,,nd is to ,,cn as  
sqrt7,,ii - ,,rr7 to sqrt7#bd7,,rr1 in  
which case ,,ne will be to ,,nd as #e,r 
to ,i2 and so on infinitely1 the        
,numbers #c1 #h1 #ae1 #bd1 c4 being     
gather'd by continual ,addition of the  
,terms of the arithmetical ,progression 
#c1 #e1 #g1 #i1 c4 ,the ,truth of all   
this ,mathematicians will easily        
examine4,m  ,now it is to be observed1  
that as when the ,sun comes to his      
,tropicks1 ,days increase and decrease  
but a very little for a great while     
together2 so when by increasing the     
distance ,,cd1 these ,angles come to    
their ,limits1 they vary their quantity 
but very little for some time together1 
and therefore a far greater number of   
the ,rays which fall upon all the       
,points ,n in the ,quadrant ,,bl1 shall 
emerge in the ,limits of these ,angles1 
than in any other ,inclinations4 ,and   
farther it is to be observed1 that the  
,rays which differ in ,refrangibility   

will have different ,limits of their    
,angles of ,emergence1 and by           
consequence according to their different
 ,degrees of ,refrangibility emerge most
 copiously in different ,angles1 and    
being separated from one another appear 
each in their proper ,colours4 ,and what
 those ,angles are may be easily        
gather'd from the foregoing ,theorem by 
,computation4  ,for in the least        
refrangible ,rays the ,sines ,i and ,r  
7as was found above7 are #ajh and #ha1  
and thence by ,computation the greatest 
,angle ,,axr will be found #db ,degrees 
and #b ,minutes1 and the least ,angle   
,,ays1 #ej ,degrees and #eg ,minutes4   
,and in the most refrangible ,rays the  
,sines ,i and ,r are #aji and #ha1 and  
thence by ,computation the greatest     
,angle ,,axr will be found #dj ,degrees 
and #ag ,minutes1 and the least ,angle  
,,ays #ed ,degrees and #g ,minutes4     
,suppose now that ,o in ,fig4 #ae4 is   
the ,spectator's ,eye1 and ,,op a ,line 
drawn parallel to the ,sun's ,rays and  

let ,,poe1 ,,pof1 ,,pog1 ,,poh1 be      
,angles of #dj ,degr4 #ag ,min4 #db     
,degr4 #b ,min4 #ej ,degr4 #eg ,min4 and
 #ed ,degr4 #g ,min4 respectively1 and  
these ,angles turned about their common 
,side ,,op1 shall with their other      
,sides ,,oe1 ,,of2 ,,og1 ,,oh1 describe 
the ,verges of two ,rain-bows ,,af1 ,,be
 and ,,chdg4 ,for if ,e1 ,f1 ,g1 ,h1 be 
drops placed any where in the conical   
,superficies described by ,,oe1 ,,of1   
,,og1 ,,oh1 and be illuminated by the   
,sun's ,rays ,,se1 ,,sf1 ,,sg1 ,,sh2 the
 ,angle ,,seo being equal to the ,angle 
,,poe1 or #dj ,degr4 #ag ,min4 shall be 
the greatest ,angle in which the most   
refrangible ,rays can after one         
,reflexion be refracted to the ,eye1 and
 therefore all the ,drops in the ,line  
,,oe shall send the most refrangible    
,rays most copiously to the ,eye1 and   
thereby strike the ,senses with the     
deepest violet ,colour in that ,region4 
,and in like manner the ,angle ,,sfo    
being equal to the ,angle ,,pof1 or #db 

,degr4 #b ,min4 shall be the greatest in
 which the least refrangible ,rays after
 one ,reflexion can emerge out of the   
,drops1 and therefore those ,rays shall 
come most copiously to the ,eye from the
 ,drops in the ,line ,,of1 and strike   
the ,senses with the deepest red ,colour
 in that ,region4 ,and by the same      
,argument1 the ,rays which have         
intermediate ,degrees of ,refrangibility
 shall come most copiously from ,drops  
between ,e and ,f1 and strike the       
,senses with the intermediate ,colours1 
in the ,order which their ,degrees of   
,refrangibility require1 that is in the 
,progress from ,e to ,f1 or from the    
inside of the ,bow to the outside in    
this order1 violet1 indigo1 blue1 green1
 yellow1 orange1 red4 ,but the violet1  
by the mixture of the white ,light of   
the ,clouds1 will appear faint and      
incline to purple4  ,illustration3      
,,fig4 #ae4  ,again1 the ,angle ,,sgo   
being equal to the ,angle ,,pog1 or #ej 
,gr4 #ea ,min4 shall be the least ,angle

 in which the least refrangible ,rays   
can after two ,reflexions emerge out of 
the ,drops1 and therefore the least     
refrangible ,rays shall come most       
copiously to the ,eye from the ,drops in
 the ,line ,,og1 and strike the ,sense  
with the deepest red in that ,region4   
,and the ,angle ,,sho being equal to the
 ,angle ,,poh1 or #ed ,gr4 #g ,min4     
shall be the least ,angle1 in which the 
most refrangible ,rays after two        
,reflexions can emerge out of the       
,drops2 and therefore those ,rays shall 
come most copiously to the ,eye from the
 ,drops in the ,line ,,oh1 and strike   
the ,senses with the deepest violet in  
that ,region4 ,and by the same          
,argument1 the ,drops in the ,regions   
between ,g and ,h shall strike the      
,sense with the intermediate ,colours in
 the ,order which their ,degrees of     
,refrangibility require1 that is1 in the
 ,progress from ,g to ,h1 or from the   
inside of the ,bow to the outside in    
this order1 red1 orange1 yellow1 green1 

blue1 indigo1 violet4 ,and since these  
four ,lines ,,oe1 ,,of1 ,,og1 ,,oh1 may 
be situated any where in the            
above-mention'd conical ,superficies2   
what is said of the ,drops and ,colours 
in these ,lines is to be understood of  
the ,drops and ,colours every where in  
those ,superficies4  ,thus shall there  
be made two ,bows of ,colours1 an       
interior and stronger1 by one ,reflexion
 in the ,drops1 and an exterior and     
fainter by two2 for the ,light becomes  
fainter by every ,reflexion4 ,and their 
,colours shall lie in a contrary ,order 
to one another1 the red of both ,bows   
bordering upon the ,space ,,gf1 which is
 between the ,bows4 ,the ,breadth of the
 interior ,bow ,,eof measured cross the 
,colours shall be #a ,degr4 #de ,min4   
and the ,breadth of the exterior ,,goh  
shall be #c ,degr4 #aj ,min4 and the    
distance between them ,,gof shall be #h 
,gr4 #ae ,min4 the greatest             
,semi-diameter of the innermost1 that   
is1 the ,angle ,,pof being #db ,gr4 #b  

,min4 and the least ,semi-diameter of   
the outermost ,,pog1 being #ej ,gr4 #eg 
,min4 ,these are the ,measures of the   
,bows1 as they would be were the ,sun   
but a ,point2 for by the ,breadth of his
 ,body1 the ,breadth of the ,bows will  
be increased1 and their ,distance       
decreased by half a ,degree1 and so the 
breadth of the interior ,iris will be #b
 ,degr4 #ae ,min4 that of the exterior  
#c ,degr4 #dj ,min4 their distance #h   
,degr4 #be ,min4 the greatest           
,semi-diameter of the interior ,bow #db 
,degr4 #ag ,min4 and the least of the   
exterior #ej ,degr4 #db ,min4 ,and such 
are the ,dimensions of the ,bows in the 
,heavens found to be very nearly1 when  
their ,colours appear strong and        
perfect4 ,for once1 by such means as ,i 
then had1 ,i measured the greatest      
,semi-diameter of the interior ,iris    
about #db ,degrees1 and the breadth of  
the red1 yellow and green in that ,iris 
#fc or #fd ,minutes1 besides the outmost
 faint red obscured by the brightness of

 the ,clouds1 for which we may allow #c 
or #d ,minutes more4 ,the breadth of the
 blue was about #dj ,minutes more       
besides the violet1 which was so much   
obscured by the brightness of the       
,clouds1 that ,i could not measure its  
breadth4 ,but supposing the breadth of  
the blue and violet together to equal   
that of the red1 yellow and green       
together1 the whole breadth of this     
,iris will be about #b-a_/d ,degrees1 as
 above4 ,the least distance between this
 ,iris and the exterior ,iris was about 
#h ,degrees and #cj ,minutes4 ,the      
exterior ,iris was broader than the     
interior1 but so faint1 especially on   
the blue side1 that ,i could not measure
 its breadth distinctly4 ,at another    
time when both ,bows appeared more      
distinct1 ,i measured the breadth of the
 interior ,iris #b ,gr4 #aj'1 and the   
breadth of the red1 yellow and green in 
the exterior ,iris1 was to the breadth  
of the same ,colours in the interior as 
#c to #b4  ,this ,explication of the    

,rain-bow is yet farther confirmed by   
the known ,experiment 7made by ,antonius
 de ,dominis and ,des-,cartes7 of       
hanging up any where in the ,sun-shine a
 ,glass ,globe filled with ,water1 and  
viewing it in such a posture1 that the  
,rays which come from the ,globe to the 
,eye may contain with the ,sun's ,rays  
an ,angle of either #db or #ej ,degrees4
 ,for if the ,angle be about #db or #dc 
,degrees1 the ,spectator 7suppose at ,o7
 shall see a full red ,colour in that   
side of the ,globe opposed to the ,sun  
as 'tis represented at ,f1 and if that  
,angle become less 7suppose by          
depressing the ,globe to ,e7 there will 
appear other ,colours1 yellow1 green and
 blue successive in the same side of the
 ,globe4 ,but if the ,angle be made     
about #ej ,degrees 7suppose by lifting  
up the ,globe to ,g7 there will appear a
 red ,colour in that side of the ,globe 
towards the ,sun1 and if the ,angle be  
made greater 7suppose by lifting up the 
,globe to ,h7 the red will turn         

successively to the other ,colours1     
yellow1 green and blue4 ,the same thing 
,i have tried1 by letting a ,globe rest1
 and raising or depressing the ,eye1 or 
otherwise moving it to make the ,angle  
of a just magnitude4  ,i have heard it  
represented1 that if the ,light of a    
,candle be refracted by a ,prism to the 
,eye2 when the blue ,colour falls upon  
the ,eye1 the ,spectator shall see red  
in the ,prism1 and when the red falls   
upon the ,eye he shall see blue2 and if 
this were certain1 the ,colours of the  
,globe and ,rain-bow ought to appear in 
a contrary order to what we find4 ,but  
the ,colours of the ,candle being very  
faint1 the mistake seems to arise from  
the difficulty of discerning what       
,colours fall on the ,eye4 ,for1 on the 
contrary1 ,i have sometimes had occasion
 to observe in the ,sun's ,light        
refracted by a ,prism1 that the         
,spectator always sees that ,colour in  
the ,prism which falls upon his ,eye4   
,and the same ,i have found true also in

 ,candle-light4 ,for when the ,prism is 
moved slowly from the ,line which is    
drawn directly from the ,candle to the  
,eye1 the red appears first in the      
,prism and then the blue1 and therefore 
each of them is seen when it falls upon 
the ,eye4 ,for the red passes over the  
,eye first1 and then the blue4  ,the    
,light which comes through drops of     
,rain by two ,refractions without any   
,reflexion1 ought to appear strongest at
 the distance of about #bf ,degrees from
 the ,sun1 and to decay gradually both  
ways as the distance from him increases 
and decreases4 ,and the same is to be   
understood of ,light transmitted through
 spherical ,hail-stones4 ,and if the    
,hail be a little flatted1 as it often  
is1 the ,light transmitted may grow so  
strong at a little less distance than   
that of #bf ,degrees1 as to form a ,halo
 about the ,sun or ,moon2 which ,halo1  
as often as the ,hail-stones are duly   
figured may be colour'd1 and then it    
must be red within by the least         

refrangible ,rays1 and blue without by  
the most refrangible ones1 especially if
 the ,hail-stones have opake ,globules  
of ,snow in their center to intercept   
the ,light within the ,halo 7as         
,hugenius has observ'd7 and make the    
inside thereof more distinctly defined  
than it would otherwise be4 ,for such   
,hail-stones1 though spherical1 by      
terminating the ,light by the ,snow1 may
 make a ,halo red within and colourless 
without1 and darker in the red than     
without1 as ,halos used to be4 ,for of  
those ,rays which pass close by the     
,snow the ,rubriform will be least      
refracted1 and so come to the ,eye in   
the directest ,lines4  ,the ,light which
 passes through a drop of ,rain after   
two ,refractions1 and three or more     
,reflexions1 is scarce strong enough to 
cause a sensible ,bow2 but in those     
,cylinders of ,ice by which ,hugenius   
explains the ,parhelia1 it may perhaps  
be sensible4   ,,prop4 ,x4 ,,prob4 ,v4  
,by the discovered ,properties of ,light

 to explain the permanent ,colours of   
,natural ,bodies4  ,these ,colours arise
 from hence1 that some natural ,bodies  
reflect some sorts of ,rays1 others     
other sorts more copiously than the     
rest4 ,minium reflects the least        
refrangible or red-making ,rays most    
copiously1 and thence appears red4      
,violets reflect the most refrangible   
most copiously1 and thence have their   
,colour1 and so of other ,bodies4 ,every
 ,body reflects the ,rays of its own    
,colour more copiously than the rest1   
and from their excess and predominance  
in the reflected ,light has its ,colour4
  ,exper4 #ag4 ,for if in the homogeneal
 ,lights obtained by the solution of the
 ,problem proposed in the fourth        
,proposition of the first ,part of this 
,book1 you place ,bodies of several     
,colours1 you will find1 as ,i have     
done1 that every ,body looks most       
splendid and luminous in the ,light of  
its own ,colour4 ,cinnaber in the       
homogeneal red ,light is most           

resplendent1 in the green ,light it is  
manifestly less resplendent1 and in the 
blue ,light still less4 ,indigo in the  
violet blue ,light is most resplendent1 
and its splendor is gradually           
diminish'd1 as it is removed thence by  
degrees through the green and yellow    
,light to the red4 ,by a ,leek the green
 ,light1 and next that the blue and     
yellow which compound green1 are more   
strongly reflected than the other       
,colours red and violet1 and so of the  
rest4 ,but to make these ,experiments   
the more manifest1 such ,bodies ought to
 be chosen as have the fullest and most 
vivid ,colours1 and two of those ,bodies
 are to be compared together4 ,thus1 for
 instance1 if ,cinnaber and ultra-marine
 blue1 or some other full blue be held  
together in the red homogeneal ,light1  
they will both appear red1 but the      
,cinnaber will appear of a strongly     
luminous and resplendent red1 and the   
ultra-marine blue of a faint obscure and
 dark red2 and if they be held together 

in the blue homogeneal ,light1 they will
 both appear blue1 but the ultra-marine 
will appear of a strongly luminous and  
resplendent blue1 and the ,cinnaber of a
 faint and dark blue4 ,which puts it out
 of dispute that the ,cinnaber reflects 
the red ,light much more copiously than 
the ultra-marine doth1 and the          
ultra-marine reflects the blue ,light   
much more copiously than the ,cinnaber  
doth4 ,the same ,experiment may be tried
 successfully with red ,lead and        
,indigo1 or with any other two colour'd 
,bodies1 if due allowance be made for   
the different strength or weakness of   
their ,colour and ,light4  ,and as the  
reason of the ,colours of natural       
,bodies is evident by these             
,experiments1 so it is farther confirmed
 and put past dispute by the two first  
,experiments of the first ,part1 whereby
 'twas proved in such ,bodies that the  
reflected ,lights which differ in       
,colours do differ also in degrees of   
,refrangibility4 ,for thence it's       

certain1 that some ,bodies reflect the  
more refrangible1 others the less       
refrangible ,rays more copiously4  ,and 
that this is not only a true reason of  
these ,colours1 but even the only       
reason1 may appear farther from this    
,consideration1 that the ,colour of     
homogeneal ,light cannot be changed by  
the ,reflexion of natural ,bodies4  ,for
 if ,bodies by ,reflexion cannot in the 
least change the ,colour of any one sort
 of ,rays1 they cannot appear colour'd  
by any other means than by reflecting   
those which either are of their own     
,colour1 or which by mixture must       
produce it4  ,but in trying ,experiments
 of this kind care must be had that the 
,light be sufficiently homogeneal4 ,for 
if ,bodies be illuminated by the        
ordinary prismatick ,colours1 they will 
appear neither of their own ,day-light  
,colours1 nor of the ,colour of the     
,light cast on them1 but of some middle 
,colour between both1 as ,i have found  
by ,experience4 ,thus red ,lead 7for    

instance7 illuminated with the ordinary 
prismatick green will not appear either 
red or green1 but orange or yellow1 or  
between yellow and green1 accordingly as
 the green ,light by which 'tis         
illuminated is more or less compounded4 
,for because red ,lead appears red when 
illuminated with white ,light1 wherein  
all sorts of ,rays are equally mix'd1   
and in the green ,light all sorts of    
,rays are not equally mix'd1 the ,excess
 of the yellow-making1 green-making and 
blue-making ,rays in the incident green 
,light1 will cause those ,rays to abound
 so much in the reflected ,light1 as to 
draw the ,colour from red towards their 
,colour4 ,and because the red ,lead     
reflects the red-making ,rays most      
copiously in proportion to their number1
 and next after them the orange-making  
and yellow-making ,rays2 these ,rays in 
the reflected ,light will be more in    
proportion to the ,light than they were 
in the incident green ,light1 and       
thereby will draw the reflected ,light  

from green towards their ,colour4 ,and  
therefore the red ,lead will appear     
neither red nor green1 but of a ,colour 
between both4  ,in transparently        
colour'd ,liquors 'tis observable1 that 
their ,colour uses to vary with their   
thickness4 ,thus1 for instance1 a red   
,liquor in a conical ,glass held between
 the ,light and the ,eye1 looks of a    
pale and dilute yellow at the bottom    
where 'tis thin1 and a little higher    
where 'tis thicker grows orange1 and    
where 'tis still thicker becomes red1   
and where 'tis thickest the red is      
deepest and darkest4 ,for it is to be   
conceiv'd that such a ,liquor stops the 
indigo-making and violet-making ,rays   
most easily1 the blue-making ,rays more 
difficultly1 the green-making ,rays     
still more difficultly1 and the         
red-making most difficultly3 ,and that  
if the thickness of the ,liquor be only 
so much as suffices to stop a competent 
number of the violet-making and         
indigo-making ,rays1 without diminishing

 much the number of the rest1 the rest  
must 7by ,prop4 #f4 ,part #b47 compound 
a pale yellow4 ,but if the ,liquor be so
 much thicker as to stop also a great   
number of the blue-making ,rays1 and    
some of the green-making1 the rest must 
compound an orange2 and where it is so  
thick as to stop also a great number of 
the green-making and a considerable     
number of the yellow-making1 the rest   
must begin to compound a red1 and this  
red must grow deeper and darker as the  
yellow-making and orange-making ,rays   
are more and more stopp'd by increasing 
the thickness of the ,liquor1 so that   
few ,rays besides the red-making can get
 through4  ,of this kind is an          
,experiment lately related to me by ,mr4
 ,halley1 who1 in diving deep into the  
,sea in a diving ,vessel1 found in a    
clear ,sun-shine ,day1 that when he was 
sunk many ,fathoms deep into the ,water 
the upper part of his ,hand on which the
 ,sun shone directly through the ,water 
and through a small ,glass ,window in   

the ,vessel appeared of a red ,colour1  
like that of a ,damask ,rose1 and the   
,water below and the under part of his  
,hand illuminated by ,light reflected   
from the ,water below look'd green4 ,for
 thence it may be gather'd1 that the    
,sea-,water reflects back the violet and
 blue-making ,rays most easily1 and lets
 the red-making ,rays pass most freely  
and copiously to great ,depths4 ,for    
thereby the ,sun's direct ,light at all 
great ,depths1 by reason of the         
predominating red-making ,rays1 must    
appear red2 and the greater the ,depth  
is1 the fuller and intenser must that   
red be4 ,and at such ,depths as the     
violet-making ,rays scarce penetrate    
unto1 the blue-making1 green-making1 and
 yellow-making ,rays being reflected    
from below more copiously than the      
red-making ones1 must compound a green4 
,now1 if there be two ,liquors of full  
,colours1 suppose a red and blue1 and   
both of them so thick as suffices to    
make their ,colours sufficiently full2  

though either ,liquor be sufficiently   
transparent apart1 yet will you not be  
able to see through both together4 ,for1
 if only the red-making ,rays pass      
through one ,liquor1 and only the       
blue-making through the other1 no ,rays 
can pass through both4 ,this ,mr4 ,hook 
tried casually with ,glass ,wedges      
filled with red and blue ,liquors1 and  
was surprized at the unexpected ,event1 
the reason of it being then unknown2    
which makes me trust the more to his    
,experiment1 though ,i have not tried it
 my self4 ,but he that would repeat it1 
must take care the ,liquors be of very  
good and full ,colours4  ,now1 whilst   
,bodies become coloured by reflecting or
 transmitting this or that sort of ,rays
 more copiously than the rest1 it is to 
be conceived that they stop and stifle  
in themselves the ,rays which they do   
not reflect or transmit4 ,for1 if ,gold 
be foliated and held between your ,eye  
and the ,light1 the ,light looks of a   
greenish blue1 and therefore massy ,gold

 lets into its ,body the blue-making    
,rays to be reflected to and fro within 
it till they be stopp'd and stifled1    
whilst it reflects the yellow-making    
outwards1 and thereby looks yellow4 ,and
 much after the same manner that ,leaf  
,gold is yellow by reflected1 and blue  
by transmitted ,light1 and massy ,gold  
is yellow in all ,positions of the ,eye2
 there are some ,liquors1 as the        
,tincture of ,lignum ,nephriticum1 and  
some sorts of ,glass which transmit one 
sort of ,light most copiously1 and      
reflect another sort1 and thereby look  
of several ,colours1 according to the   
,position of the ,eye to the ,light4    
,but1 if these ,liquors or ,glasses were
 so thick and massy that no ,light could
 get through them1 ,i question not but  
they would like all other opake ,bodies 
appear of one and the same ,colour in   
all ,positions of the ,eye1 though this 
,i cannot yet affirm by ,experience4    
,for all colour'd ,bodies1 so far as my 
,observation reaches1 may be seen       

through if made sufficiently thin1 and  
therefore are in some measure           
transparent1 and differ only in degrees 
of ,transparency from tinged transparent
 ,liquors2 these ,liquors1 as well as   
those ,bodies1 by a sufficient          
,thickness becoming opake4 ,a           
transparent ,body which looks of any    
,colour by transmitted ,light1 may also 
look of the same ,colour by reflected   
,light1 the ,light of that ,colour being
 reflected by the farther ,surface of   
the ,body1 or by the ,air beyond it4    
,and then the reflected ,colour will be 
diminished1 and perhaps cease1 by making
 the ,body very thick1 and pitching it  
on the backside to diminish the         
,reflexion of its farther ,surface1 so  
that the ,light reflected from the      
tinging ,particles may predominate4 ,in 
such ,cases1 the ,colour of the         
reflected ,light will be apt to vary    
from that of the ,light transmitted4    
,but whence it is that tinged ,bodies   
and ,liquors reflect some sort of ,rays1

 and intromit or transmit other sorts1  
shall be said in the next ,book4 ,in    
this ,proposition ,i content my self to 
have put it past dispute1 that ,bodies  
have such ,properties1 and thence appear
 colour'd4   ,,prop4 ,,xi4 ,,prob4 ,,vi4
  ,by mixing colour'd ,lights to        
compound a beam of ,light of the same   
,colour and ,nature with a beam of the  
,sun's direct ,light1 and therein to    
experience the ,truth of the foregoing  
,propositions4  ,illustration3 ,,fig4   
#af4  ,let ,,abc abc in ,fig4 #af4      
represent a ,prism1 by which the ,sun's 
,light let into a dark ,chamber through 
the ,hole ,f1 may be refracted towards  
the ,lens ,,mn1 and paint upon it at p1 
q1 r1 s1 and t1 the usual ,colours      
violet1 blue1 green1 yellow1 and red1   
and let the diverging ,rays by the      
,refraction of this ,lens converge again
 towards ,x1 and there1 by the mixture  
of all those their ,colours1 compound a 
white according to what was shewn above4
 ,then let another ,prism ,,deg deg1    

parallel to the former1 be placed at ,x1
 to refract that white ,light upwards   
towards ,y4 ,let the refracting ,angles 
of the ,prisms1 and their distances from
 the ,lens be equal1 so that the ,rays  
which converged from the ,lens towards  
,x1 and without ,refraction1 would there
 have crossed and diverged again1 may by
 the ,refraction of the second ,prism be
 reduced into ,parallelism and diverge  
no more4 ,for then those ,rays will     
recompose a beam of white ,light ,,xy4  
,if the refracting ,angle of either     
,prism be the bigger1 that ,prism must  
be so much the nearer to the ,lens4 ,you
 will know when the ,prisms and the     
,lens are well set together1 by         
observing if the beam of ,light ,,xy1   
which comes out of the second ,prism be 
perfectly white to the very edges of the
 ,light1 and at all distances from the  
,prism continue perfectly and totally   
white like a beam of the ,sun's ,light4 
,for till this happens1 the ,position of
 the ,prisms and ,lens to one another   

must be corrected2 and then if by the   
help of a long beam of ,wood1 as is     
represented in the ,figure1 or by a     
,tube1 or some other such ,instrument1  
made for that ,purpose1 they be made    
fast in that ,situation1 you may try all
 the same ,experiments in this          
compounded beam of ,light ,,xy1 which   
have been made in the ,sun's direct     
,light4 ,for this compounded beam of    
,light has the same appearance1 and is  
endow'd with all the same ,properties   
with a direct beam of the ,sun's ,light1
 so far as my ,observation reaches4 ,and
 in trying ,experiments in this beam you
 may by stopping any of the ,colours1 p1
 q1 r1 s1 and t1 at the ,lens1 see how  
the ,colours produced in the            
,experiments are no other than those    
which the ,rays had at the ,lens before 
they entered the ,composition of this   
,beam3 ,and by consequence1 that they   
arise not from any new ,modifications of
 the ,light by ,refractions and         
,reflexions1 but from the various       

,separations and ,mixtures of the ,rays 
originally endow'd with their           
colour-making ,qualities4  ,so1 for     
instance1 having with a ,lens #d-a_/d   
,inches broad1 and two ,prisms on either
 hand #f-a_/d ,feet distant from the    
,lens1 made such a beam of compounded   
,light2 to examine the reason of the    
,colours made by ,prisms1 ,i refracted  
this compounded beam of ,light ,,xy with
 another ,prism ,,hik kh1 and thereby   
cast the usual ,prismatick ,colours     
,,pqrst upon the ,paper ,,lv placed     
behind4 ,and then by stopping any of the
 ,colours p1 q1 r1 s1 t1 at the ,lens1  
,i found that the same ,colour would    
vanish at the ,paper4 ,so if the ,purple
 p was stopp'd at the ,lens1 the ,purple
 ,p upon the ,paper would vanish1 and   
the rest of the ,colours would remain   
unalter'd1 unless perhaps the blue1 so  
far as some purple latent in it at the  
,lens might be separated from it by the 
following ,refractions4 ,and so by      
intercepting the green upon the ,lens1  

the green ,r upon the ,paper would      
vanish1 and so of the rest2 which       
plainly shews1 that as the white beam of
 ,light ,,xy was compounded of several  
,lights variously colour'd at the ,lens1
 so the ,colours which afterwards emerge
 out of it by new ,refractions are no   
other than those of which its ,whiteness
 was compounded4 ,the ,refraction of the
 ,prism ,,hik kh generates the ,colours 
,,pqrst upon the ,paper1 not by changing
 the colorific ,qualities of the ,rays1 
but by separating the ,rays which had   
the very same colorific ,qualities      
before they enter'd the ,composition of 
the refracted beam of white ,light ,,xy4
 ,for otherwise the ,rays which were of 
one ,colour at the ,lens might be of    
another upon the ,paper1 contrary to    
what we find4  ,so again1 to examine the
 reason of the ,colours of natural      
,bodies1 ,i placed such ,bodies in the  
,beam of ,light ,,xy1 and found that    
they all appeared there of those their  
own ,colours which they have in         

,day-light1 and that those ,colours     
depend upon the ,rays which had the same
 ,colours at the ,lens before they      
enter'd the ,composition of that beam4  
,thus1 for instance1 ,cinnaber          
illuminated by this beam appears of the 
same red ,colour as in ,day-light2 and  
if at the ,lens you intercept the       
green-making and blue-making ,rays1 its 
redness will become more full and       
lively3 ,but if you there intercept the 
red-making ,rays1 it will not any longer
 appear red1 but become yellow or green1
 or of some other ,colour1 according to 
the sorts of ,rays which you do not     
intercept4 ,so ,gold in this ,light ,,xy
 appears of the same yellow ,colour as  
in ,day-light1 but by intercepting at   
the ,lens a due ,quantity of the        
yellow-making ,rays it will appear white
 like ,silver 7as ,i have tried7 which  
shews that its yellowness arises from   
the ,excess of the intercepted ,rays    
tinging that ,whiteness with their      
,colour when they are let pass4 ,so the 

,infusion of ,lignum ,nephriticum 7as ,i
 have also tried7 when held in this beam
 of ,light ,,xy1 looks blue by the      
reflected ,part of the ,light1 and red  
by the transmitted ,part of it1 as when 
'tis view'd in ,day-light2 but if you   
intercept the blue at the ,lens the     
,infusion will lose its reflected blue  
,colour1 whilst its transmitted red     
remains perfect1 and by the loss of some
 blue-making ,rays1 wherewith it was    
allay'd1 becomes more intense and full4 
,and1 on the contrary1 if the red and   
orange-making ,rays be intercepted at   
the ,lens1 the ,infusion will lose its  
transmitted red1 whilst its blue will   
remain and become more full and perfect4
 ,which shews1 that the ,infusion does  
not tinge the ,rays with blue and red1  
but only transmits those most copiously 
which were red-making before1 and       
reflects those most copiously which were
 blue-making before4 ,and after the same
 manner may the ,reasons of other       
,phaenomena be examined1 by trying them 

in this artificial beam of ,light ,,xy4 
,,footnotes3  ,i ,see p4 #ei4  ,j ,see  
our ,author's ,lect4 ,optic4 ,part ,,ii4
 ,sect4 ,,ii4 p4 #bci4  ,k ,as is done  
in our ,author's ,lect4 ,optic4 ,part   
,i4 ,sect4 ,,iii4 and ,,iv4 and ,part   
,,ii4 ,sect4 ,,ii4  ,l ,see our         
,author's ,lect4 ,optic4 ,part ,,ii4    
,sect4 ,,ii4 pag4 #bfi1 c4  ,m ,this is 
demonstrated in our ,author's ,lect4    
,optic4 ,part ,i4 ,sect4 ,,iv4 ,prop4   
#ce and #cf4     ,,the  ,,second ,,book 
,,of  ,,opticks     ,,part ,i4          
,observations concerning the            
,reflexions1 ,refractions1 and ,colours 
of thin transparent ,bodies4   ,it has  
been observed by others1 that           
transparent ,substances1 as ,glass1     
,water1 ,air1 c4 when made very thin by 
being blown into ,bubbles1 or otherwise 
formed into ,plates1 do exhibit various 
,colours according to their various     
thinness1 altho' at a greater thickness 
they appear very clear and colourless4  
,in the former ,book ,i forbore to treat

 of these ,colours1 because they seemed 
of a more difficult ,consideration1 and 
were not necessary for establishing the 
,properties of ,light there discoursed  
of4 ,but because they may conduce to    
farther ,discoveries for compleating the
 ,theory of ,light1 especially as to the
 constitution of the parts of natural   
,bodies1 on which their ,colours or     
,transparency depend2 ,i have here set  
down an account of them4 ,to render this
 ,discourse short and distinct1 ,i have 
first described the principal of my     
,observations1 and then consider'd and  
made use of them4 ,the ,observations are
 these4  ,obs4 #a4 ,compressing two     
,prisms hard together that their sides  
7which by chance were a very little     
convex7 might somewhere touch one       
another3 ,i found the place in which    
they touched to become absolutely       
transparent1 as if they had there been  
one continued piece of ,glass4 ,for when
 the ,light fell so obliquely on the    
,air1 which in other places was between 

them1 as to be all reflected2 it seemed 
in that place of contact to be wholly   
transmitted1 insomuch that when look'd  
upon1 it appeared like a black or dark  
spot1 by reason that little or no       
sensible ,light was reflected from      
thence1 as from other places2 and when  
looked through it seemed 7as it were7 a 
hole in that ,air which was formed into 
a thin ,plate1 by being compress'd      
between the ,glasses4 ,and through this 
hole ,objects that were beyond might be 
seen distinctly1 which could not at all 
be seen through other parts of the      
,glasses where the ,air was interjacent4
 ,although the ,glasses were a little   
convex1 yet this transparent spot was of
 a considerable breadth1 which breadth  
seemed principally to proceed from the  
yielding inwards of the parts of the    
,glasses1 by reason of their mutual     
pressure4 ,for by pressing them very    
hard together it would become much      
broader than otherwise4  ,obs4 #b4 ,when
 the ,plate of ,air1 by turning the     

,prisms about their common ,axis1 became
 so little inclined to the incident     
,rays1 that some of them began to be    
transmitted1 there arose in it many     
slender ,arcs of ,colours which at first
 were shaped almost like the ,conchoid1 
as you see them delineated in the first 
,figure4 ,and by continuing the ,motion 
of the ,prisms1 these ,arcs increased   
and bended more and more about the said 
transparent spot1 till they were        
compleated into ,circles or ,rings      
incompassing it1 and afterwards         
continually grew more and more          
contracted4  ,illustration3 ,,fig4 #a4  
,these ,arcs at their first appearance  
were of a violet and blue ,colour1 and  
between them were white ,arcs of        
,circles1 which presently by continuing 
the ,motion of the ,prisms became a     
little tinged in their inward ,limbs    
with red and yellow1 and to their       
outward ,limbs the blue was adjacent4   
,so that the order of these ,colours    
from the central dark spot1 was at that 

time white1 blue1 violet2 black1 red1   
orange1 yellow1 white1 blue1 violet1 c4 
,but the yellow and red were much       
fainter than the blue and violet4  ,the 
,motion of the ,prisms about their ,axis
 being continued1 these ,colours        
contracted more and more1 shrinking     
towards the whiteness on either side of 
it1 until they totally vanished into it4
 ,and then the ,circles in those parts  
appear'd black and white1 without any   
other ,colours intermix'd4 ,but by      
farther moving the ,prisms about1 the   
,colours again emerged out of the       
whiteness1 the violet and blue at its   
inward ,limb1 and at its outward ,limb  
the red and yellow4 ,so that now their  
order from the central ,spot was white1 
yellow1 red2 black2 violet1 blue1 white1
 yellow1 red1 c4 contrary to what it was
 before4  ,obs4 #c4 ,when the ,rings or 
some parts of them appeared only black  
and white1 they were very distinct and  
well defined1 and the blackness seemed  
as intense as that of the central ,spot4

 ,also in the ,borders of the ,rings1   
where the ,colours began to emerge out  
of the whiteness1 they were pretty      
distinct1 which made them visible to a  
very great multitude4 ,i have sometimes 
number'd above thirty ,successions      
7reckoning every black and white ,ring  
for one ,succession7 and seen more of   
them1 which by reason of their smalness 
,i could not number4 ,but in other      
,positions of the ,prisms1 at which the 
,rings appeared of many ,colours1 ,i    
could not distinguish above eight or    
nine of them1 and the ,exterior of those
 were very confused and dilute4  ,in    
these two ,observations to see the      
,rings distinct1 and without any other  
,colour than ,black and white1 ,i found 
it necessary to hold my ,eye at a good  
distance from them4 ,for by approaching 
nearer1 although in the same inclination
 of my ,eye to the ,plane of the ,rings1
 there emerged a bluish ,colour out of  
the white1 which by dilating it self    
more and more into the black1 render'd  

the ,circles less distinct1 and left the
 white a little tinged with red and     
yellow4 ,i found also by looking through
 a slit or oblong hole1 which was       
narrower than the pupil of my ,eye1 and 
held close to it parallel to the        
,prisms1 ,i could see the ,circles much 
distincter and visible to a far greater 
number than otherwise4  ,obs4 #d4 ,to   
observe more nicely the order of the    
,colours which arose out of the white   
,circles as the ,rays became less and   
less inclined to the ,plate of ,air2 ,i 
took two ,object-glasses1 the one a     
,plano-convex for a fourteen ,foot      
,telescope1 and the other a large double
 ,convex for one of about fifty ,foot2  
and upon this1 laying the other with its
 plane side downwards1 ,i pressed them  
slowly together1 to make the ,colours   
successively emerge in the middle of the
 ,circles1 and then slowly lifted the   
upper ,glass from the lower to make them
 successively vanish again in the same  
place4 ,the ,colour1 which by pressing  

the ,glasses together1 emerged last in  
the middle of the other ,colours1 would 
upon its first appearance look like a   
,circle of a ,colour almost uniform from
 the circumference to the center and by 
compressing the ,glasses still more1    
grow continually broader until a new    
,colour emerged in its center1 and      
thereby it became a ,ring encompassing  
that new ,colour4 ,and by compressing   
the ,glasses still more1 the diameter of
 this ,ring would increase1 and the     
breadth of its ,orbit or ,perimeter     
decrease until another new ,colour      
emerged in the center of the last3 ,and 
so on until a third1 a fourth1 a fifth1 
and other following new ,colours        
successively emerged there1 and became  
,rings encompassing the innermost       
,colour1 the last of which was the black
 ,spot4 ,and1 on the contrary1 by       
lifting up the upper ,glass from the    
lower1 the diameter of the ,rings would 
decrease1 and the breadth of their      
,orbit increase1 until their ,colours   

reached successively to the center2 and 
then they being of a considerable       
breadth1 ,i could more easily discern   
and distinguish their ,species than     
before4 ,and by this means ,i observ'd  
their ,succession and ,quantity to be as
 followeth4  ,next to the pellucid      
central ,spot made by the contact of the
 ,glasses succeeded blue1 white1 yellow1
 and red4 ,the blue was so little in    
quantity1 that ,i could not discern it  
in the ,circles made by the ,prisms1 nor
 could ,i well distinguish any violet in
 it1 but the yellow and red were pretty 
copious1 and seemed about as much in    
extent as the white1 and four or five   
times more than the blue4 ,the next     
,circuit in order of ,colours           
immediately encompassing these were     
violet1 blue1 green1 yellow1 and red3   
and these were all of them copious and  
vivid1 excepting the green1 which was   
very little in quantity1 and seemed much
 more faint and dilute than the other   
,colours4 ,of the other four1 the violet

 was the least in extent1 and the blue  
less than the yellow or red4 ,the third 
,circuit or ,order was purple1 blue1    
green1 yellow1 and red2 in which the    
purple seemed more reddish than the     
violet in the former ,circuit1 and the  
green was much more conspicuous1 being  
as brisk and copious as any of the other
 ,colours1 except the yellow1 but the   
red began to be a little faded1         
inclining very much to purple4 ,after   
this succeeded the fourth ,circuit of   
green and red4 ,the green was very      
copious and lively1 inclining on the one
 side to blue1 and on the other side to 
yellow4 ,but in this fourth ,circuit    
there was neither violet1 blue1 nor     
yellow1 and the red was very imperfect  
and dirty4 ,also the succeeding ,colours
 became more and more imperfect and     
dilute1 till after three or four        
revolutions they ended in perfect       
whiteness4 ,their form1 when the        
,glasses were most compress'd so as to  
make the black ,spot appear in the      

center1 is delineated in the second     
,figure2 where a1 b1 c1 d1 e3 f1 g1 h1  
i1 k3 l1 m1 n1 o1 p3 q1 r3 s1 t3 v1 x3  
y1 z1 denote the ,colours reckon'd in   
order from the center1 black1 blue1     
white1 yellow1 red3 violet1 blue1 green1
 yellow1 red3 purple1 blue1 green1      
yellow1 red3 green1 red3 greenish blue1 
red3 greenish blue1 pale red3 greenish  
blue1 reddish white4  ,illustration3    
,,fig4 #b4  ,obs4 #e4 ,to determine the 
interval of the ,glasses1 or thickness  
of the interjacent ,air1 by which each  
,colour was produced1 ,i measured the   
,diameters of the first six ,rings at   
the most lucid part of their ,orbits1   
and squaring them1 ,i found their       
,squares to be in the arithmetical      
,progression of the odd ,numbers1 #a1   
#c1 #e1 #g1 #i1 #aa4 ,and since one of  
these ,glasses was plane1 and the other 
spherical1 their ,intervals at those    
,rings must be in the same ,progression4
 ,i measured also the ,diameters of the 
dark or faint ,rings between the more   

lucid ,colours1 and found their ,squares
 to be in the arithmetical ,progression 
of the even ,numbers1 #b1 #d1 #f1 #h1   
#aj1 #ab4 ,and it being very nice and   
difficult to take these measures        
exactly2 ,i repeated them divers times  
at divers parts of the ,glasses1 that by
 their ,agreement ,i might be confirmed 
in them4 ,and the same method ,i used in
 determining some others of the         
following ,observations4  ,obs4 #f4 ,the
 ,diameter of the sixth ,ring at the    
most lucid part of its ,orbit was       
#eh_/ajj parts of an ,inch1 and the     
,diameter of the ,sphere on which the   
double convex ,object-glass was ground  
was about #ajb ,feet1 and hence ,i      
gathered the thickness of the ,air or   
,aereal ,interval of the ,glasses at    
that ,ring4 ,but some time after1       
suspecting that in making this          
,observation ,i had not determined the  
,diameter of the ,sphere with sufficient
 accurateness1 and being uncertain      
whether the ,plano-convex ,glass was    

truly plane1 and not something concave  
or convex on that side which ,i         
accounted plane2 and whether ,i had not 
pressed the ,glasses together1 as ,i    
often did1 to make them touch2 7,for by 
pressing such ,glasses together their   
parts easily yield inwards1 and the     
,rings thereby become sensibly broader  
than they would be1 did the ,glasses    
keep their ,figures47 ,i repeated the   
,experiment1 and found the ,diameter of 
the sixth lucid ,ring about #ee_/ajj    
parts of an ,inch4 ,i repeated the      
,experiment also with such an           
,object-glass of another ,telescope as  
,i had at hand4 ,this was a double      
,convex ground on both sides to one and 
the same ,sphere1 and its ,focus was    
distant from it #hc-b_/e ,inches4 ,and  
thence1 if the ,sines of ,incidence and 
,refraction of the bright yellow ,light 
be assumed in proportion as #aa to #ag1 
the ,diameter of the ,sphere to which   
the ,glass was figured will by          
computation be found #ahb ,inches4 ,this

 ,glass ,i laid upon a flat one1 so that
 the black ,spot appeared in the middle 
of the ,rings of ,colours without any   
other ,pressure than that of the weight 
of the ,glass4 ,and now measuring the   
,diameter of the fifth dark ,circle as  
accurately as ,i could1 ,i found it the 
fifth part of an ,inch precisely4 ,this 
,measure was taken with the points of a 
pair of ,compasses on the upper ,surface
 on the upper ,glass1 and my ,eye was   
about eight or nine ,inches distance    
from the ,glass1 almost perpendicularly 
over it1 and the ,glass was #a_/f of an 
,inch thick1 and thence it is easy to   
collect that the true ,diameter of the  
,ring between the ,glasses was greater  
than its measur'd ,diameter above the   
,glasses in the ,proportion of #hj to   
#gi1 or thereabouts1 and by consequence 
equal to #af_/gi parts of an ,inch1 and 
its true ,semi-diameter equal to #h_/gi 
parts4 ,now as the ,diameter of the     
,sphere 7#ahb ,inches7 is to the        
,semi-diameter of this fifth dark ,ring 

7#h_/gi parts of an ,inch7 so is this   
,semi-diameter to the thickness of the  
,air at this fifth dark ,ring2 which is 
therefore #cb_/efgica or #ajj_/aggdghd4 
,parts of an ,inch2 and the fifth ,part 
thereof1 viz4 the #a_/hhgci ,part of an 
,inch1 is the ,thickness of the ,air at 
the first of these dark ,rings4  ,the   
same ,experiment ,i repeated with       
another double convex ,object-glass     
ground on both sides to one and the same
 ,sphere4 ,its ,focus was distant from  
it #afh-a_/b ,inches1 and therefore the 
,diameter of that ,sphere was #ahd      
,inches4 ,this ,glass being laid upon   
the same plain ,glass1 the ,diameter of 
the fifth of the dark ,rings1 when the  
black ,spot in their ,center appear'd   
plainly without pressing the ,glasses1  
was by the measure of the ,compasses    
upon the upper ,glass #aba_/fjj ,parts  
of an ,inch1 and by consequence between 
the ,glasses it was #abbb_/fjjj3 ,for   
the upper ,glass was #a_/h of an ,inch  
thick1 and my ,eye was distant from it  

#h ,inches4 ,and a third proportional to
 half this from the ,diameter of the    
,sphere is #e_/hhhej ,parts of an ,inch4
 ,this is therefore the ,thickness of   
the ,air at this ,ring1 and a fifth     
,part thereof1 viz4 the #a_/hhhejth     
,part of an ,inch is the ,thickness     
thereof at the first of the ,rings1 as  
above4  ,i tried the same ,thing1 by    
laying these ,object-glasses upon flat  
,pieces of a broken ,looking-glass1 and 
found the same ,measures of the ,rings3 
,which makes me rely upon them till they
 can be determin'd more accurately by   
,glasses ground to larger ,spheres1     
though in such ,glasses greater care    
must be taken of a true ,plane4  ,these 
,dimensions were taken1 when my ,eye was
 placed almost perpendicularly over the 
,glasses1 being about an ,inch1 or an   
,inch and a quarter1 distant from the   
incident ,rays1 and eight ,inches       
distant from the ,glass2 so that the    
,rays were inclined to the ,glass in an 
,angle of about four ,degrees4 ,whence  

by the following ,observation you will  
understand1 that had the ,rays been     
perpendicular to the ,glasses1 the      
,thickness of the ,air at these ,rings  
would have been less in the ,proportion 
of the ,radius to the ,secant of four   
,degrees1 that is1 of #ajjjj to #ajjbd4 
,let the ,thicknesses found be therefore
 diminish'd in this ,proportion1 and    
they will become #a_/hhieb and          
#a_/hijfc1 or 7to use the nearest round 
,number7 the #a_/hijjjth ,part of an    
,inch4 ,this is the ,thickness of the   
,air at the darkest ,part of the first  
dark ,ring made by perpendicular ,rays2 
and half this ,thickness multiplied by  
the ,progression1 #a1 #c1 #e1 #g1 #i1   
#aa1 c4 gives the ,thicknesses of the   
,air at the most luminous ,parts of all 
the brightest ,rings1 viz4 #a_/aghjjj1  
#c_/aghjjj1 #e_/aghjjj1 #g_/aghjjj1 c4  
their arithmetical ,means #b_/aghjjj1   
#d_/aghjjj1 #f_/aghjjj1 c4 being its    
,thicknesses at the darkest ,parts of   
all the dark ones4  ,obs4 #g4 ,the      

,rings were least1 when my ,eye was     
placed perpendicularly over the ,glasses
 in the ,axis of the ,rings3 ,and when  
,i view'd them obliquely they became    
bigger1 continually swelling as ,i      
removed my ,eye farther from the ,axis4 
,and partly by measuring the ,diameter  
of the same ,circle at several          
,obliquities of my ,eye1 partly by other
 ,means1 as also by making use of the   
two ,prisms for very great ,obliquities1
 ,i found its ,diameter1 and            
consequently the ,thickness of the ,air 
at its ,perimeter in all those          
,obliquities to be very nearly in the   
,proportions express'd in this ,table4  
----------------------------------------
------------------- ,angle of ,incidence
 ,angle of ,refraction ,diameter        
,thickness         on                   
into         of the     of the       the
 ,air4            the ,air4             
,ring4      ,air4                       
----------------------------------------
-------------------     ,deg4    ,min4  

#jj      #jj          #jj      #jj      
#aj        #aj                          
#jf      #bf          #aj      #jj      
#aj-a_/ac   #aj-b_/ac                   
#ab      #de          #bj      #jj      
#aj-a_/c    #aj-b_/c                    
#ah      #di          #cj      #jj      
#aj-c_/d    #aa-a_/b                    
#bd      #cj          #dj      #jj      
#aa-b_/e    #ac                         
#bi      #cg          #ej      #jj      
#ab-a_/b    #ae-a_/b                    
#cc      #eh          #fj      #jj      
#ad        #bj                          
#ce      #dg          #fe      #jj      
#ae-a_/d    #bc-a_/d                    
#cg      #ai          #gj      #jj      
#af-d_/e    #bh-a_/d                    
#ch      #cc          #ge      #jj      
#ai-a_/d    #cg                         
#ci      #bg          #hj      #jj      
#bb-f_/g    #eb-a_/d                    
#dj      #jj          #he      #jj      
#bi        #hd-a_/ab                    
#dj      #aa          #ij      #jj      

#ce       #abb-a_/b                     
----------------------------------------
-------------------  ,in the two first  
,columns are express'd the ,obliquities 
of the incident and emergent ,rays to   
the ,plate of the ,air1 that is1 their  
,angles of ,incidence and ,refraction4  
,in the third ,column the ,diameter of  
any colour'd ,ring at those ,obliquities
 is expressed in ,parts1 of which ten   
constitute that ,diameter when the ,rays
 are perpendicular4 ,and in the fourth  
,column the ,thickness of the ,air at   
the ,circumference of that ,ring is     
expressed in ,parts1 of which also ten  
constitute its ,thickness when the ,rays
 are perpendicular4  ,and from these    
,measures ,i seem to gather this ,rule3 
,that the ,thickness of the ,air is     
proportional to the ,secant of an       
,angle1 whose ,sine is a certain mean   
,proportional between the ,sines of     
,incidence and ,refraction4 ,and that   
mean ,proportional1 so far as by these  
,measures ,i can determine it1 is the   

first of an hundred and six arithmetical
 mean ,proportionals between those      
,sines counted from the bigger ,sine1   
that is1 from the ,sine of ,refraction  
when the ,refraction is made out of the 
,glass into the ,plate of ,air1 or from 
the ,sine of ,incidence when the        
,refraction is made out of the ,plate of
 ,air into the ,glass4  ,obs4 #h4 ,the  
dark ,spot in the middle of the ,rings  
increased also by the ,obliquation of   
the ,eye1 although almost insensibly4   
,but1 if instead of the ,object-glasses 
the ,prisms were made use of1 its       
,increase was more manifest when viewed 
so obliquely that no ,colours appear'd  
about it4 ,it was least when the ,rays  
were incident most obliquely on the     
interjacent ,air1 and as the obliquity  
decreased it increased more and more    
until the colour'd ,rings appear'd1 and 
then decreased again1 but not so much as
 it increased before4 ,and hence it is  
evident1 that the ,transparency was not 
only at the absolute ,contact of the    

,glasses1 but also where they had some  
little ,interval4 ,i have sometimes     
observed the ,diameter of that ,spot to 
be between half and two fifth parts of  
the ,diameter of the exterior           
,circumference of the red in the first  
,circuit or ,revolution of ,colours when
 view'd almost perpendicularly2 whereas 
when view'd obliquely it hath wholly    
vanish'd and become opake and white like
 the other parts of the ,glass2 whence  
it may be collected that the ,glasses   
did then scarcely1 or not at all1 touch 
one another1 and that their ,interval at
 the perimeter of that ,spot when view'd
 perpendicularly was about a fifth or   
sixth part of their ,interval at the    
circumference of the said red4  ,obs4   
#i4 ,by looking through the two         
contiguous ,object-glasses1 ,i found    
that the interjacent ,air exhibited     
,rings of ,colours1 as well by          
transmitting ,light as by reflecting it4
 ,the central ,spot was now white1 and  
from it the order of the ,colours were  

yellowish red2 black1 violet1 blue1     
white1 yellow1 red2 violet1 blue1 green1
 yellow1 red1 c4 ,but these ,colours    
were very faint and dilute1 unless when 
the ,light was trajected very obliquely 
through the ,glasses3 ,for by that means
 they became pretty vivid4 ,only the    
first yellowish red1 like the blue in   
the fourth ,observation1 was so little  
and faint as scarcely to be discern'd4  
,comparing the colour'd ,rings made by  
,reflexion1 with these made by          
transmission of the ,light2 ,i found    
that white was opposite to black1 red to
 blue1 yellow to violet1 and green to a 
,compound of red and violet4 ,that is1  
those parts of the ,glass were black    
when looked through1 which when looked  
upon appeared white1 and on the         
contrary4 ,and so those which in one    
case exhibited blue1 did in the other   
case exhibit red4 ,and the like of the  
other ,colours4 ,the manner you have    
represented in the third ,figure1 where 
,,ab1 ,,cd1 are the ,surfaces of the    

,glasses contiguous at ,e1 and the black
 ,lines between them are their          
,distances in arithmetical ,progression1
 and the ,colours written above are seen
 by reflected ,light1 and those below by
 ,light transmitted 7p4 #bji74  ,obs4   
#aj4 ,wetting the ,object-glasses a     
little at their edges1 the ,water crept 
in slowly between them1 and the ,circles
 thereby became less and the ,colours   
more faint3 ,insomuch that as the ,water
 crept along1 one half of them at which 
it first arrived would appear broken off
 from the other half1 and contracted    
into a less ,room4 ,by measuring them ,i
 found the ,proportions of their        
,diameters to the ,diameters of the like
 ,circles made by ,air to be about seven
 to eight1 and consequently the         
,intervals of the ,glasses at like      
,circles1 caused by those two ,mediums  
,water and ,air1 are as about three to  
four4 ,perhaps it may be a general      
,rule1 ,that if any other ,medium more  
or less dense than ,water be compress'd 

between the ,glasses1 their ,intervals  
at the ,rings caused thereby will be to 
their ,intervals caused by interjacent  
,air1 as the ,sines are which measure   
the ,refraction made out of that ,medium
 into ,air4  ,obs4 #aa4 ,when the ,water
 was between the ,glasses1 if ,i pressed
 the upper ,glass variously at its edges
 to make the ,rings move nimbly from one
 place to another1 a little white ,spot 
would immediately follow the center of  
them1 which upon creeping in of the     
ambient ,water into that place would    
presently vanish4 ,its appearance was   
such as interjacent ,air would have     
caused1 and it exhibited the same       
,colours4 ,but it was not air1 for where
 any ,bubbles of ,air were in the ,water
 they would not vanish4 ,the ,reflexion 
must have rather been caused by a       
subtiler ,medium1 which could recede    
through the ,glasses at the creeping in 
of the ,water4  ,obs4 #ab4 ,these       
,observations were made in the open     
,air4 ,but farther to examine the       

,effects of colour'd ,light falling on  
the ,glasses1 ,i darken'd the ,room1 and
 view'd them by ,reflexion of the       
,colours of a ,prism cast on a ,sheet of
 white ,paper1 my ,eye being so placed  
that ,i could see the colour'd ,paper by
 ,reflexion in the ,glasses1 as in a    
,looking-glass4 ,and by this means the  
,rings became distincter and visible to 
a far greater number than in the open   
,air4 ,i have sometimes seen more than  
twenty of them1 whereas in the open ,air
 ,i could not discern above eight or    
nine4  ,illustration3 ,,fig4 #c4  ,obs4 
#ac4 ,appointing an ,assistant to move  
the ,prism to and fro about its ,axis1  
that all the ,colours might successively
 fall on that part of the ,paper which  
,i saw by ,reflexion from that part of  
the ,glasses1 where the ,circles        
appear'd1 so that all the ,colours might
 be successively reflected from the     
,circles to my ,eye1 whilst ,i held it  
immovable1 ,i found the ,circles which  
the red ,light made to be manifestly    

bigger than those which were made by the
 blue and violet4 ,and it was very      
pleasant to see them gradually swell or 
contract accordingly as the ,colour of  
the ,light was changed4 ,the ,interval  
of the ,glasses at any of the ,rings    
when they were made by the utmost red   
,light1 was to their ,interval at the   
same ,ring when made by the utmost      
violet1 greater than as #c to #b1 and   
less than as #ac to #h4 ,by the most of 
my ,observations it was as #ad to #i4   
,and this ,proportion seem'd very nearly
 the same in all ,obliquities of my     
,eye2 unless when two ,prisms were made 
use of instead of the ,object-glasses4  
,for then at a certain great obliquity  
of my ,eye1 the ,rings made by the      
several ,colours seem'd equal1 and at a 
greater obliquity those made by the     
violet would be greater than the same   
,rings made by the red3 the ,refraction 
of the ,prism in this case causing the  
most refrangible ,rays to fall more     
obliquely on that plate of the ,air than

 the least refrangible ones4 ,thus the  
,experiment succeeded in the colour'd   
,light1 which was sufficiently strong   
and copious to make the ,rings sensible4
 ,and thence it may be gather'd1 that if
 the most refrangible and least         
refrangible ,rays had been copious      
enough to make the ,rings sensible      
without the mixture of other ,rays1 the 
,proportion which here was #ad to #i    
would have been a little greater1       
suppose #ad-a_/d or #ad-a_/c to #i4     
,obs4 #ad4 ,whilst the ,prism was turn'd
 about its ,axis with an uniform        
,motion1 to make all the several        
,colours fall successively upon the     
,object-glasses1 and thereby to make the
 ,rings contract and dilate3 ,the       
,contraction or ,dilatation of each     
,ring thus made by the variation of its 
,colour was swiftest in the red1 and    
slowest in the violet1 and in the       
intermediate ,colours it had            
intermediate degrees of ,celerity4      
,comparing the quantity of ,contraction 

and ,dilatation made by all the degrees 
of each ,colour1 ,i found that it was   
greatest in the red2 less in the yellow1
 still less in the blue1 and least in   
the violet4 ,and to make as just an     
,estimation as ,i could of the          
,proportions of their ,contractions or  
,dilatations1 ,i observ'd that the whole
 ,contraction or ,dilatation of the     
,diameter of any ,ring made by all the  
degrees of red1 was to that of the      
,diameter of the same ,ring made by all 
the degrees of violet1 as about four to 
three1 or five to four1 and that when   
the ,light was of the middle ,colour    
between yellow and green1 the ,diameter 
of the ,ring was very nearly an         
arithmetical ,mean between the greatest 
,diameter of the same ,ring made by the 
outmost red1 and the least ,diameter    
thereof made by the outmost violet3     
,contrary to what happens in the        
,colours of the oblong ,spectrum made by
 the ,refraction of a ,prism1 where the 
red is most contracted1 the violet most 

expanded1 and in the midst of all the   
,colours is the ,confine of green and   
blue4 ,and hence ,i seem to collect that
 the thicknesses of the ,air between the
 ,glasses there1 where the ,ring is     
successively made by the limits of the  
five principal ,colours 7red1 yellow1   
green1 blue1 violet7 in order 7that is1 
by the extreme red1 by the limit of red 
and yellow in the middle of the orange1 
by the limit of yellow and green1 by the
 limit of green and blue1 by the limit  
of blue and violet in the middle of the 
indigo1 and by the extreme violet7 are  
to one another very nearly as the sixth 
lengths of a ,chord which found the     
,notes in a sixth ,major1 sol1 la1 mi1  
fa1 sol1 la4 ,but it agrees something   
better with the ,observation to say1    
that the thicknesses of the ,air between
 the ,glasses there1 where the ,rings   
are successively made by the limits of  
the seven ,colours1 red1 orange1 yellow1
 green1 blue1 indigo1 violet in order1  
are to one another as the ,cube ,roots  

of the ,squares of the eight lengths of 
a ,chord1 which found the ,notes in an  
eighth1 sol1 la1 fa1 sol1 la1 mi1 fa1   
sol2 that is1 as the ,cube ,roots of the
 ,squares of the ,numbers1 #a1 #h_/i1   
#e_/f1 #c_/d1 #b_/c1 #c_/e1 #i_/af1     
#a_/b4  ,obs4 #ae4 ,these ,rings were   
not of various ,colours like those made 
in the open ,air1 but appeared all over 
of that prismatick ,colour only with    
which they were illuminated4 ,and by    
projecting the prismatick ,colours      
immediately upon the ,glasses1 ,i found 
that the ,light which fell on the dark  
,spaces which were between the ,colour'd
 ,rings was transmitted through the     
,glasses without any variation of       
,colour4 ,for on a white ,paper placed  
behind1 it would paint ,rings of the    
same ,colour with those which were      
reflected1 and of the bigness of their  
immediate ,spaces4 ,and from thence the 
origin of these ,rings is manifest2     
namely1 that the ,air between the       
,glasses1 according to its various      

thickness1 is disposed in some places to
 reflect1 and in others to transmit the 
,light of any one ,colour 7as you may   
see represented in the fourth ,figure7  
and in the same place to reflect that of
 one ,colour where it transmits that of 
another4  ,illustration3 ,,fig4 #d4     
,obs4 #af4 ,the ,squares of the         
,diameters of these ,rings made by any  
prismatick ,colour were in arithmetical 
,progression1 as in the fifth           
,observation4 ,and the ,diameter of the 
sixth ,circle1 when made by the citrine 
yellow1 and viewed almost               
perpendicularly was about #eh_/ajj parts
 of an ,inch1 or a little less1         
agreeable to the sixth ,observation4    
,the precedent ,observations were made  
with a rarer thin ,medium1 terminated by
 a denser1 such as was ,air or ,water   
compress'd between two ,glasses4 ,in    
those that follow are set down the      
,appearances of a denser ,medium thin'd 
within a rarer1 such as are ,plates of  
,muscovy ,glass1 ,bubbles of ,water1 and

 some other thin ,substances terminated 
on all sides with air4  ,obs4 #ag4 ,if a
 ,bubble be blown with ,water first made
 tenacious by dissolving a little ,soap 
in it1 'tis a common ,observation1 that 
after a while it will appear tinged with
 a great variety of ,colours4 ,to defend
 these ,bubbles from being agitated by  
the external ,air 7whereby their        
,colours are irregularly moved one among
 another1 so that no accurate           
,observation can be made of them17 as   
soon as ,i had blown any of them ,i     
cover'd it with a clear ,glass1 and by  
that means its ,colours emerged in a    
very regular order1 like so many        
concentrick ,rings encompassing the top 
of the ,bubble4 ,and as the ,bubble grew
 thinner by the continual subsiding of  
the ,water1 these ,rings dilated slowly 
and overspread the whole ,bubble1       
descending in order to the bottom of it1
 where they vanish'd successively4 ,in  
the mean while1 after all the ,colours  
were emerged at the top1 there grew in  

the center of the ,rings a small round  
black ,spot1 like that in the first     
,observation1 which continually dilated 
it self till it became sometimes more   
than #a_/b or #c_/d of an ,inch in      
breadth before the ,bubble broke4 ,at   
first ,i thought there had been no      
,light reflected from the ,water in that
 place1 but observing it more curiously1
 ,i saw within it several smaller round 
,spots1 which appeared much blacker and 
darker than the rest1 whereby ,i knew   
that there was some ,reflexion at the   
other places which were not so dark as  
those ,spots4 ,and by farther ,tryal ,i 
found that ,i could see the ,images of  
some things 7as of a ,candle or the     
,sun7 very faintly reflected1 not only  
from the great black ,spot1 but also    
from the little darker ,spots which were
 within it4  ,besides the aforesaid     
colour'd ,rings there would often appear
 small ,spots of ,colours1 ascending and
 descending up and down the sides of the
 ,bubble1 by reason of some             

,inequalities in the subsiding of the   
,water4 ,and sometimes small black      
,spots generated at the sides would     
ascend up to the larger black ,spot at  
the top of the ,bubble1 and unite with  
it4  ,obs4 #ah4 ,because the ,colours of
 these ,bubbles were more extended and  
lively than those of the ,air thinn'd   
between two ,glasses1 and so more easy  
to be distinguish'd1 ,i shall here give 
you a farther description of their      
order1 as they were observ'd in viewing 
them by ,reflexion of the ,skies when of
 a white ,colour1 whilst a black        
substance was placed behind the ,bubble4
 ,and they were these1 red1 blue2 red1  
blue2 red1 blue2 red1 green2 red1       
yellow1 green1 blue1 purple2 red1       
yellow1 green1 blue1 violet2 red1       
yellow1 white1 blue1 black4  ,the three 
first ,successions of red and blue were 
very dilute and dirty1 especially the   
first1 where the red seem'd in a manner 
to be white4 ,among these there was     
scarce any other ,colour sensible       

besides red and blue1 only the blues    
7and principally the second blue7       
inclined a little to green4  ,the fourth
 red was also dilute and dirty1 but not 
so much as the former three2 after that 
succeeded little or no yellow1 but a    
copious green1 which at first inclined a
 little to yellow1 and then became a    
pretty brisk and good willow green1 and 
afterwards changed to a bluish ,colour2 
but there succeeded neither blue nor    
violet4  ,the fifth red at first        
inclined very much to purple1 and       
afterwards became more bright and brisk1
 but yet not very pure4 ,this was       
succeeded with a very bright and intense
 yellow1 which was but little in        
quantity1 and soon chang'd to green3    
,but that green was copious and         
something more pure1 deep and lively1   
than the former green4 ,after that      
follow'd an excellent blue of a bright  
,sky-colour1 and then a purple1 which   
was less in quantity than the blue1 and 
much inclined to red4  ,the sixth red   

was at first of a very fair and lively  
scarlet1 and soon after of a brighter   
,colour1 being very pure and brisk1 and 
the best of all the reds4 ,then after a 
lively orange follow'd an intense bright
 and copious yellow1 which was also the 
best of all the yellows1 and this       
changed first to a greenish yellow1 and 
then to a greenish blue2 but the green  
between the yellow and the blue1 was    
very little and dilute1 seeming rather a
 greenish white than a green4 ,the blue 
which succeeded became very good1 and of
 a very bright ,sky-colour1 but yet     
something inferior to the former blue2  
and the violet was intense and deep with
 little or no redness in it4 ,and less  
in quantity than the blue4  ,in the last
 red appeared a tincture of scarlet next
 to violet1 which soon changed to a     
brighter ,colour1 inclining to an       
orange2 and the yellow which follow'd   
was at first pretty good and lively1 but
 afterwards it grew more dilute until by
 degrees it ended in perfect whiteness4 

,and this whiteness1 if the ,water was  
very tenacious and well-temper'd1 would 
slowly spread and dilate it self over   
the greater part of the ,bubble2        
continually growing paler at the top1   
where at length it would crack in many  
places1 and those cracks1 as they       
dilated1 would appear of a pretty good1 
but yet obscure and dark ,sky-colour2   
the white between the blue ,spots       
diminishing1 until it resembled the     
,threds of an irregular ,net-work1 and  
soon after vanish'd1 and left all the   
upper part of the ,bubble of the said   
dark blue ,colour4 ,and this ,colour1   
after the aforesaid manner1 dilated it  
self downwards1 until sometimes it hath 
overspread the whole ,bubble4 ,in the   
mean while at the top1 which was of a   
darker blue than the bottom1 and        
appear'd also full of many round blue   
,spots1 something darker than the rest1 
there would emerge one or more very     
black ,spots1 and within those1 other   
,spots of an intenser blackness1 which  

,i mention'd in the former ,observation2
 and these continually dilated          
themselves until the ,bubble broke4  ,if
 the ,water was not very tenacious1 the 
black ,spots would break forth in the   
white1 without any sensible intervention
 of the blue4 ,and sometimes they would 
break forth within the precedent yellow1
 or red1 or perhaps within the blue of  
the second order1 before the            
intermediate ,colours had time to       
display themselves4  ,by this           
description you may perceive how great  
an affinity these ,colours have with    
those of ,air described in the fourth   
,observation1 although set down in a    
contrary order1 by reason that they     
begin to appear when the ,bubble is     
thickest1 and are most conveniently     
reckon'd from the lowest and thickest   
part of the ,bubble upwards4  ,obs4 #ai4
 ,viewing in several oblique ,positions 
of my ,eye the ,rings of ,colours       
emerging on the top of the ,bubble1 ,i  
found that they were sensibly dilated by

 increasing the obliquity1 but yet not  
so much by far as those made by thinn'd 
,air in the seventh ,observation4 ,for  
there they were dilated so much as1 when
 view'd most obliquely1 to arrive at a  
part of the ,plate more than twelve     
times thicker than that where they      
appear'd when viewed perpendicularly2   
whereas in this case the thickness of   
the ,water1 at which they arrived when  
viewed most obliquely1 was to that      
thickness which exhibited them by       
perpendicular ,rays1 something less than
 as #h to #e4 ,by the best of my        
,observations it was between #ae and    
#ae-a_/b to #aj2 an increase about #bd  
times less than in the other case4      
,sometimes the ,bubble would become of  
an uniform thickness all over1 except at
 the top of it near the black ,spot1 as 
,i knew1 because it would exhibit the   
same appearance of ,colours in all      
,positions of the ,eye4 ,and then the   
,colours which were seen at its apparent
 circumference by the obliquest ,rays1  

would be different from those that were 
seen in other places1 by ,rays less     
oblique to it4 ,and divers ,spectators  
might see the same part of it of        
differing ,colours1 by viewing it at    
very differing ,obliquities4 ,now       
observing how much the ,colours at the  
same places of the ,bubble1 or at divers
 places of equal thickness1 were varied 
by the several ,obliquities of the      
,rays2 by the assistance of the #dth1   
#adth1 #afth and #ahth ,observations1 as
 they are hereafter explain'd1 ,i       
collect the thickness of the ,water     
requisite to exhibit any one and the    
same ,colour1 at several ,obliquities1  
to be very nearly in the ,proportion    
expressed in this ,table4               
----------------------------------------
-----------   ,incidence on             
,refraction into   ,thickness of    the 
,water4        the ,water4       the    
,water4                                 
----------------------------------------
-----------    ,deg4    ,min4      ,deg4

    ,min4                               
#jj     #jj         #jj     #jj         
#aj                                     
#ae     #jj         #aa     #aa         
#aj-a_/d                                
#cj     #jj         #bb      #a         
#aj-d_/e                                
#de     #jj         #cb      #b         
#aa-d_/e                                
#fj     #jj         #dj     #cj         
#ac                                     
#ge     #jj         #df     #be         
#ad-a_/b                                
#ij     #jj         #dh     #ce         
#ae-a_/e                                
----------------------------------------
-----------  ,in the two first ,columns 
are express'd the ,obliquities of the   
,rays to the ,superficies of the ,water1
 that is1 their ,angles of ,incidence   
and ,refraction4 ,where ,i suppose1 that
 the ,sines which measure them are in   
round ,numbers1 as #c to #d1 though     
probably the ,dissolution of ,soap in   
the ,water1 may a little alter its      

refractive ,virtue4 ,in the third       
,column1 the ,thickness of the ,bubble1 
at which any one ,colour is exhibited in
 those several ,obliquities1 is         
express'd in ,parts1 of which ten       
constitute its ,thickness when the ,rays
 are perpendicular4 ,and the ,rule found
 by the seventh ,observation agrees well
 with these ,measures1 if duly apply'd2 
namely1 that the ,thickness of a ,plate 
of ,water requisite to exhibit one and  
the same ,colour at several ,obliquities
 of the ,eye1 is proportional to the    
,secant of an ,angle1 whose ,sine is the
 first of an hundred and six            
arithmetical mean ,proportionals between
 the ,sines of ,incidence and           
,refraction counted from the lesser     
,sine1 that is1 from the ,sine of       
,refraction when the ,refraction is made
 out of ,air into ,water1 otherwise from
 the ,sine of ,incidence4  ,i have      
sometimes observ'd1 that the ,colours   
which arise on polish'd ,steel by       
heating it1 or on ,bell-metal1 and some 

other metalline ,substances1 when melted
 and pour'd on the ,ground1 where they  
may cool in the open ,air1 have1 like   
the ,colours of ,water-bubbles1 been a  
little changed by viewing them at divers
 ,obliquities1 and particularly that a  
deep blue1 or violet1 when view'd very  
obliquely1 hath been changed to a deep  
red4 ,but the ,changes of these ,colours
 are not so great and sensible as of    
those made by ,water4 ,for the ,scoria1 
or vitrified ,part of the ,metal1 which 
most ,metals when heated or melted do   
continually protrude1 and send out to   
their ,surface1 and which by covering   
the ,metals in form of a thin glassy    
,skin1 causes these ,colours1 is much   
denser than ,water2 and ,i find that the
 ,change made by the ,obliquation of the
 ,eye is least in ,colours of the       
densest thin ,substances4  ,obs4 #bj4   
,as in the ninth ,observation1 so here1 
the ,bubble1 by transmitted ,light1     
appear'd of a contrary ,colour to that1 
which it exhibited by ,reflexion4 ,thus 

when the ,bubble being look'd on by the 
,light of the ,clouds reflected from it1
 seemed red at its apparent             
,circumference1 if the ,clouds at the   
same time1 or immediately after1 were   
view'd through it1 the ,colour at its   
,circumference would be blue4 ,and1 on  
the contrary1 when by reflected ,light  
it appeared blue1 it would appear red by
 transmitted ,light4  ,obs4 #ba4 ,by    
wetting very thin ,plates of ,muscovy   
,glass1 whose thinness made the like    
,colours appear1 the ,colours became    
more faint and languid1 especially by   
wetting the ,plates on that side        
opposite to the ,eye3 ,but ,i could not 
perceive any variation of their         
,species4 ,so then the thickness of a   
,plate requisite to produce any ,colour1
 depends only on the density of the     
,plate1 and not on that of the ambient  
,medium4 ,and hence1 by the #ajth and   
#afth ,observations1 may be known the   
thickness which ,bubbles of ,water1 or  
,plates of ,muscovy ,glass1 or other    

,substances1 have at any ,colour        
produced by them4  ,obs4 #bb4 ,a thin   
transparent ,body1 which is denser than 
its ambient ,medium1 exhibits more brisk
 and vivid ,colours than that which is  
so much rarer2 as ,i have particularly  
observed in the ,air and ,glass4 ,for   
blowing ,glass very thin at a ,lamp     
,furnace1 those ,plates encompassed with
 ,air did exhibit ,colours much more    
vivid than those of ,air made thin      
between two ,glasses4  ,obs4 #bc4       
,comparing the quantity of ,light       
reflected from the several ,rings1 ,i   
found that it was most copious from the 
first or inmost1 and in the exterior    
,rings became gradually less and less4  
,also the whiteness of the first ,ring  
was stronger than that reflected from   
those parts of the thin ,medium or      
,plate which were without the ,rings2 as
 ,i could manifestly perceive by viewing
 at a distance the ,rings made by the   
two ,object-glasses2 or by comparing two
 ,bubbles of ,water blown at distant    

,times1 in the first of which the       
,whiteness appear'd1 which succeeded all
 the ,colours1 and in the other1 the    
,whiteness which preceded them all4     
,obs4 #bd4 ,when the two ,object-glasses
 were lay'd upon one another1 so as to  
make the ,rings of the ,colours appear1 
though with my naked ,eye ,i could not  
discern above eight or nine of those    
,rings1 yet by viewing them through a   
,prism ,i have seen a far greater       
,multitude1 insomuch that ,i could      
number more than forty1 besides many    
others1 that were so very small and     
close together1 that ,i could not keep  
my ,eye steady on them severally so as  
to number them1 but by their ,extent ,i 
have sometimes estimated them to be more
 than an hundred4 ,and ,i believe the   
,experiment may be improved to the      
,discovery of far greater ,numbers4 ,for
 they seem to be really unlimited1      
though visible only so far as they can  
be separated by the ,refraction of the  
,prism1 as ,i shall hereafter explain4  

,illustration3 ,,fig4 #e4  ,but it was  
but one side of these ,rings1 namely1   
that towards which the ,refraction was  
made1 which by that ,refraction was     
render'd distinct1 and the other side   
became more confused than when view'd by
 the naked ,eye1 insomuch that there ,i 
could not discern above one or two1 and 
sometimes none of those ,rings1 of which
 ,i could discern eight or nine with my 
naked ,eye4 ,and their ,segments or     
,arcs1 which on the other side appear'd 
so numerous1 for the most part exceeded 
not the third ,part of a ,circle4 ,if   
the ,refraction was very great1 or the  
,prism very distant from the            
,object-glasses1 the middle ,part of    
those ,arcs became also confused1 so as 
to disappear and constitute an even     
,whiteness1 whilst on either side their 
,ends1 as also the whole ,arcs farthest 
from the ,center1 became distincter than
 before1 appearing in the ,form as you  
see them design'd in the fifth ,figure4 
,the ,arcs1 where they seem'd           

distinctest1 were only white and black  
successively1 without any other ,colours
 intermix'd4 ,but in other ,places there
 appeared ,colours1 whose ,order was    
inverted by the refraction in such      
manner1 that if ,i first held the ,prism
 very near the ,object-glasses1 and then
 gradually removed it farther off       
towards my ,eye1 the ,colours of the    
#b;d1 #c;d1 #dth1 and following ,rings1 
shrunk towards the white that emerged   
between them1 until they wholly vanish'd
 into it at the middle of the ,arcs1 and
 afterwards emerged again in a contrary 
,order4 ,but at the ,ends of the ,arcs  
they retain'd their ,order unchanged4   
,i have sometimes so lay'd one          
,object-glass upon the other1 that to   
the naked ,eye they have all over seem'd
 uniformly white1 without the least     
,appearance of any of the colour'd      
,rings2 and yet by viewing them through 
a ,prism1 great ,multitudes of those    
,rings have discover'd themselves4 ,and 
in like manner ,plates of ,muscovy      

,glass1 and ,bubbles of ,glass blown at 
a ,lamp-,furnace1 which were not so thin
 as to exhibit any ,colours to the naked
 ,eye1 have through the ,prism exhibited
 a great ,variety of them ranged        
irregularly up and down in the ,form of 
,waves4 ,and so ,bubbles of ,water1     
before they began to exhibit their      
,colours to the naked ,eye of a         
,bystander1 have appeared through a     
,prism1 girded about with many parallel 
and horizontal ,rings2 to produce which 
,effect1 it was necessary to hold the   
,prism parallel1 or very nearly parallel
 to the ,horizon1 and to dispose it so  
that the ,rays might be refracted       
upwards4     ,,the  ,,second ,,book     
,,of  ,,opticks   ,,part ,,ii4  ,remarks
 upon the foregoing ,observations4      
,having given my ,observations of these 
,colours1 before ,i make use of them to 
unfold the ,causes of the ,colours of   
natural ,bodies1 it is convenient that  
by the simplest of them1 such as are the
 #b;d1 #c;d1 #dth1 #ith1 #abth1 #ahth1  

#bjth1 and #bdth1 ,i first explain the  
more compounded4 ,and first to shew how 
the ,colours in the fourth and          
eighteenth ,observations are produced1  
let there be taken in any ,right ,line  
from the ,point ,y1 in ,fig4 #f4 the    
,lengths ,,ya1 ,,yb1 ,,yc1 ,,yd1 ,,ye1  
,,yf1 ,,yg1 ,,yh1 in proportion to one  
another1 as the ,cube-,roots of the     
,squares of the ,numbers1 #a_/b1 #i_/af1
 #c_/e1 #b_/c1 #c_/d1 #e_/f1 #h_/i1 #a1 
whereby the ,lengths of a ,musical      
,chord to sound all the ,notes in an    
eighth are represented2 that is1 in the 
,proportion of the ,numbers #fcjj1      
#fhad1 #gaad1 #gfca1 #hbee1 #hhee1      
#ibdc1 #ajjjj4 ,and at the ,points ,a1  
,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h1 let         
,perpendiculars ,a,greek3 a1 ,b,greek3  
b1 c4 be erected1 by whose ,intervals   
the ,extent of the several ,colours set 
underneath against them1 is to be       
represented4 ,then divide the ,line     
,a,greek3 a in such ,proportion as the  
,numbers #a1 #b1 #c1 #e1 #f1 #g1 #i1    

#aj1 #aa1 c4 set at the ,points of      
,division denote4 ,and through those    
,divisions from ,y draw ,lines #a;,i1   
#b,k1 #c,l1 #e,m1 #f,n1 #g,o1 c4  ,now1 
if ,a#b be supposed to represent the    
,thickness of any thin transparent      
,body1 at which the outmost ,violet is  
most copiously reflected in the first   
,ring1 or ,series of ,colours1 then by  
the #acth ,observation1 ,,hk will       
represent its ,thickness1 at which the  
utmost ,red is most copiously reflected 
in the same ,series4 ,also by the #eth  
and #afth ,observations1 ,a#f and ,,hn  
will denote the ,thicknesses at which   
those extreme ,colours are most         
copiously reflected in the second       
,series1 and ,a#aj and ,,hq the         
,thicknesses at which they are most     
copiously reflected in the third        
,series1 and so on4 ,and the ,thickness 
at which any of the intermediate        
,colours are reflected most copiously1  
will1 according to the #adth            
,observation1 be defined by the distance

 of the ,line ,,ah from the intermediate
 parts of the ,lines #b,k1 #f,n1 #aj,q1 
c4 against which the ,names of those    
,colours are written below4             
,illustration3 ,,fig4 #f4  ,but farther1
 to define the ,latitude of these       
,colours in each ,ring or ,series1 let  
,a#a design the least thickness1 and    
,a#c the greatest thickness1 at which   
the extreme violet in the first ,series 
is reflected1 and let ,,hi1 and ,,hl1   
design the like limits for the extreme  
red1 and let the intermediate ,colours  
be limited by the intermediate parts of 
the ,lines #a;,i1 and #c,l1 against     
which the ,names of those ,colours are  
written1 and so on3 ,but yet with this  
caution1 that the ,reflexions be        
supposed strongest at the intermediate  
,spaces1 #b,k1 #f,n1 #aj,q1 c4 and from 
thence to decrease gradually towards    
these limits1 #a;,i1 #c,l1 #e,m1 #g,o1  
c4 on either side2 where you must not   
conceive them to be precisely limited1  
but to decay indefinitely4 ,and whereas 

,i have assign'd the same ,latitude to  
every ,series1 ,i did it1 because       
although the ,colours in the first      
,series seem to be a little broader than
 the rest1 by reason of a stronger      
,reflexion there1 yet that inequality is
 so insensible as scarcely to be        
determin'd by ,observation4  ,now       
according to this ,description1         
conceiving that the ,rays originally of 
several ,colours are by turns reflected 
at the ,spaces #a;,i1 ,l#c1 #e,m1 ,o#g1 
#i,,pr#aa1 c4 and transmitted at the    
,spaces ,,ahi#a1 #c,,lm#e1 #g,,op#i1 c4 
it is easy to know what ,colour must in 
the open ,air be exhibited at any       
thickness of a transparent thin ,body4  
,for if a ,ruler be applied parallel to 
,,ah1 at that distance from it by which 
the thickness of the ,body is           
represented1 the alternate ,spaces      
#a;,,il#c1 #e,,mo#g1 c4 which it        
crosseth will denote the reflected      
original ,colours1 of which the ,colour 
exhibited in the open ,air is           

compounded4 ,thus if the constitution of
 the green in the third ,series of      
,colours be desired1 apply the ,ruler as
 you see at ,greek3 prsph1 and by its   
passing through some of the blue at     
,greek3 p and yellow at ,greek3 s1 as   
well as through the green at ,greek3 r1 
you may conclude that the green         
exhibited at that thickness of the ,body
 is principally constituted of original 
green1 but not without a mixture of some
 blue and yellow4  ,by this means you   
may know how the ,colours from the      
center of the ,rings outward ought to   
succeed in order as they were described 
in the #dth and #ahth ,observations4    
,for if you move the ,ruler gradually   
from ,,ah through all distances1 having 
pass'd over the first ,space which      
denotes little or no ,reflexion to be   
made by thinnest ,substances1 it will   
first arrive at #a the violet1 and then 
very quickly at the blue and green1     
which together with that violet compound
 blue1 and then at the yellow and red1  

by whose farther addition that blue is  
converted into whiteness1 which         
whiteness continues during the transit  
of the edge of the ,ruler from ,i to #c1
 and after that by the successive       
deficience of its component ,colours1   
turns first to compound yellow1 and then
 to red1 and last of all the red ceaseth
 at ,l4 ,then begin the ,colours of the 
second ,series1 which succeed in order  
during the transit of the edge of the   
,ruler from #e to ,o1 and are more      
lively than before1 because more        
expanded and severed4 ,and for the same 
reason instead of the former white there
 intercedes between the blue and yellow 
a mixture of orange1 yellow1 green1 blue
 and indigo1 all which together ought to
 exhibit a dilute and imperfect green4  
,so the ,colours of the third ,series   
all succeed in order2 first1 the violet1
 which a little interferes with the red 
of the second order1 and is thereby     
inclined to a reddish purple2 then the  
blue and green1 which are less mix'd    

with other ,colours1 and consequently   
more lively than before1 especially the 
green3 ,then follows the yellow1 some of
 which towards the green is distinct and
 good1 but that part of it towards the  
succeeding red1 as also that red is     
mix'd with the violet and blue of the   
fourth ,series1 whereby various degrees 
of red very much inclining to purple are
 compounded4 ,this violet and blue1     
which should succeed this red1 being    
mixed with1 and hidden in it1 there     
succeeds a green4 ,and this at first is 
much inclined to blue1 but soon becomes 
a good green1 the only unmix'd and      
lively ,colour in this fourth ,series4  
,for as it verges towards the yellow1 it
 begins to interfere with the ,colours  
of the fifth ,series1 by whose mixture  
the succeeding yellow and red are very  
much diluted and made dirty1 especially 
the yellow1 which being the weaker      
,colour is scarce able to shew it self4 
,after this the several ,series         
interfere more and more1 and their      

,colours become more and more           
intermix'd1 till after three or four    
more revolutions 7in which the red and  
blue predominate by turns7 all sorts of 
,colours are in all places pretty       
equally blended1 and compound an even   
whiteness4  ,and since by the #aeth     
,observation the ,rays endued with one  
,colour are transmitted1 where those of 
another ,colour are reflected1 the      
reason of the ,colours made by the      
transmitted ,light in the #ith and #bjth
 ,observations is from hence evident4   
,if not only the ,order and ,species of 
these ,colours1 but also the precise    
thickness of the ,plate1 or thin ,body  
at which they are exhibited1 be desired 
in parts of an ,inch1 that may be also  
obtained by assistance of the #fth or   
#afth ,observations4 ,for according to  
those ,observations the thickness of the
 thinned ,air1 which between two        
,glasses exhibited the most luminous    
parts of the first six ,rings were      
#a_/aghjjj1 #c_/aghjjj1 #e_/aghjjj1     

#g_/aghjjj1 #i_/aghjjj1 #aa_/aghjjj     
parts of an ,inch4 ,suppose the ,light  
reflected most copiously at these       
thicknesses be the bright citrine       
yellow1 or confine of yellow and orange1
 and these thicknesses will be ,f,greek3
 l1 ,f,greek3 m1 ,f,greek3 u1 ,f,greek3 
x1 ,f,greek3 o1 ,f,greek3 t4 ,and this  
being known1 it is easy to determine    
what thickness of ,air is represented by
 ,g,greek3 ph1 or by any other distance 
of the ,ruler from ,,ah4  ,but farther1 
since by the #ajth ,observation the     
thickness of ,air was to the thickness  
of ,water1 which between the same       
,glasses exhibited the same ,colour1 as 
#d to #c1 and by the #bast ,observation 
the ,colours of thin ,bodies are not    
varied by varying the ambient ,medium2  
the thickness of a ,bubble of ,water1   
exhibiting any ,colour1 will be #c_/d of
 the thickness of ,air producing the    
same ,colour4 ,and so according to the  
same #ajth and #bast ,observations1 the 
thickness of a ,plate of ,glass1 whose  

,refraction of the mean refrangible     
,ray1 is measured by the proportion of  
the ,sines #ca to #bj1 may be #bj_/ca of
 the thickness of ,air producing the    
same ,colours2 and the like of other    
,mediums4 ,i do not affirm1 that this   
proportion of #bj to #ca1 holds in all  
the ,rays2 for the ,sines of other sorts
 of ,rays have other ,proportions4 ,but 
the differences of those ,proportions   
are so little that ,i do not here       
consider them4 ,on these ,grounds ,i    
have composed the following ,table1     
wherein the thickness of ,air1 ,water1  
and ,glass1 at which each ,colour is    
most intense and specifick1 is expressed
 in parts of an ,inch divided into ten  
hundred thousand equal parts4  ,now if  
this ,table be compared with the #fth   
,scheme1 you will there see the         
constitution of each ,colour1 as to its 
,ingredients1 or the original ,colours  
of which it is compounded1 and thence be
 enabled to judge of its ,intenseness or
 ,imperfection2 which may suffice in    

explication of the #dth and #ahth       
,observations1 unless it be farther     
desired to delineate the manner how the 
,colours appear1 when the two           
,object-glasses are laid upon one       
another4 ,to do which1 let there be     
described a large ,arc of a ,circle1 and
 a streight ,line which may touch that  
,arc1 and parallel to that ,tangent     
several occult ,lines1 at such distances
 from it1 as the ,numbers set against   
the several ,colours in the ,table      
denote4 ,for the ,arc1 and its ,tangent1
 will represent the ,superficies of the 
,glasses terminating the interjacent    
,air2 and the places where the occult   
,lines cut the ,arc will show at what   
distances from the center1 or ,point of 
contact1 each ,colour is reflected4     
,the thickness of colour'd ,plates and  
,particles of                           
_/                                      
,air4      ,water4     ,glass4          
-----------------------------           
,very black          #a_/b      #c_/h   

#aj_/ca                           ,black
             #a          #c_/d          
#bj_/ca                                 
,beginning of                           
,black           #b        #a-a_/b      
#a-b_/g    ,their ,colours of the       
,blue              #b-b_/e    #a-d_/e   
#a-aa_/bb  first ,order1                
,white             #e-a_/d    #c-g_/h   
#c-b_/e                                 
,yellow            #g-a_/i    #e-a_/c   
#d-c_/e                                 
,orange            #h        #f         
#e-a_/f                           ,red  
#i        #f-c_/d     #e-d_/e           
-----------------------------           
,violet           #aa-a_/f    #h-c_/h   
#g-a_/e                                 
,indigo           #ab-e_/f    #i-e_/h   
#h-b_/aa                          ,blue 
#ad        #aj-a_/b    #i               
,green            #ae-a_/h   #aa-b_/c   
#i-e_/g    ,of the second order1        
,yellow           #af-b_/g   #ab-a_/e   
#aj-b_/e                                

,orange           #ag-b_/i   #ac        
#aa-a_/i                                
,bright red       #ah-a_/c   #ac-c_/d   
#aa-e_/f                                
,scarlet          #ai-b_/c   #ad-c_/d   
#ab-b_/c                                
-----------------------------           
,purple           #ba       #ae-c_/d    
#ac-aa_/bj                              
,indigo           #bb-a_/aj  #af-d_/g   
#ad-a_/d                           ,blue
             #bc-b_/e   #ag-aa_/bj      
#ae-a_/aj   ,of the third ,order1       
,green            #be-a_/e   #ah-i_/aj  
#af-a_/d                                
,yellow           #bg-a_/g   #bj-a_/c   
#ag-a_/b                           ,red 
#bi       #ba-c_/d    #ah-e_/g          
,bluish red       #cb       #bd         
#bj-b_/c                                
-----------------------------           
,bluish green     #cd       #be-a_/b    
#bb                               ,green
            #ce-b_/g   #bf-a_/b         
#bb-c_/d    ,of the fourth ,order1      

,yellowish green  #cf       #bg         
#bc-b_/i                           ,red 
#dj-a_/c   #cj-a_/d    #bf              
-----------------------------           
,greenish blue    #df       #cd-a_/b    
#bi-b_/c    ,of the fifth ,order1       
,red              #eb-a_/b   #ci-c_/h   
#cd                                     
-----------------------------           
,greenish blue    #eh-c_/d   #dd        
#ch        ,of the sixth ,order1    ,red
              #fe       #dh-c_/d    #db 
----------------------------- ,of the   
seventh ,order1  ,greenish blue    #ga  
#ec-a_/d    #de-d_/e                    
,ruddy ,white      #gg       #eg-c_/d   
#di-b_/c                                
-----------------------------  ,there   
are also other ,uses of this ,table3    
,for by its assistance the thickness of 
the ,bubble in the #aith ,observation   
was determin'd by the ,colours which it 
exhibited4 ,and so the bigness of the   
parts of natural ,bodies may be         
conjectured by their ,colours1 as shall 

be hereafter shewn4 ,also1 if two or    
more very thin ,plates be laid one upon 
another1 so as to compose one ,plate    
equalling them all in thickness1 the    
resulting ,colour may be hereby         
determin'd4 ,for instance1 ,mr4 ,hook   
observed1 as is mentioned in his        
,micrographia1 that a faint yellow      
,plate of ,muscovy ,glass laid upon a   
blue one1 constituted a very deep       
purple4 ,the yellow of the first ,order 
is a faint one1 and the thickness of the
 ,plate exhibiting it1 according to the 
,table is #d-c_/e1 to which add #i1 the 
thickness exhibiting blue of the second 
,order1 and the ,sum will be #ac-c_/e1  
which is the thickness exhibiting the   
purple of the third ,order4  ,to        
explain1 in the next place1 the         
circumstances of the #b;d and #c;d      
,observations2 that is1 how the ,rings  
of the ,colours may 7by turning the     
,prisms about their common ,axis the    
contrary way to that expressed in those 
,observations7 be converted into white  

and black ,rings1 and afterwards into   
,rings of ,colours again1 the ,colours  
of each ,ring lying now in an inverted  
order2 it must be remember'd1 that those
 ,rings of ,colours are dilated by the  
obliquation of the ,rays to the ,air    
which intercedes the ,glasses1 and that 
according to the ,table in the #gth     
,observation1 their ,dilatation or      
,increase of their ,diameter is most    
manifest and speedy when they are       
obliquest4 ,now the ,rays of yellow     
being more refracted by the first       
,superficies of the said ,air than those
 of red1 are thereby made more oblique  
to the second ,superficies1 at which    
they are reflected to produce the       
colour'd ,rings1 and consequently the   
yellow ,circle in each ,ring will be    
more dilated than the red2 and the      
,excess of its ,dilatation will be so   
much the greater1 by how much the       
greater is the obliquity of the ,rays1  
until at last it become of equal extent 
with the red of the same ,ring4 ,and for

 the same reason the green1 blue and    
violet1 will be also so much dilated by 
the still greater obliquity of their    
,rays1 as to become all very nearly of  
equal extent with the red1 that is1     
equally distant from the center of the  
,rings4 ,and then all the ,colours of   
the same ,ring must be co-incident1 and 
by their mixture exhibit a white ,ring4 
,and these white ,rings must have black 
and dark ,rings between them1 because   
they do not spread and interfere with   
one another1 as before4 ,and for that   
reason also they must become distincter1
 and visible to far greater numbers4    
,but yet the violet being obliquest will
 be something more dilated1 in          
proportion to its extent1 than the other
 ,colours1 and so very apt to appear at 
the exterior ,verges of the white4      
,afterwards1 by a greater obliquity of  
the ,rays1 the violet and blue become   
more sensibly dilated than the red and  
yellow1 and so being farther removed    
from the center of the ,rings1 the      

,colours must emerge out of the white in
 an order contrary to that which they   
had before2 the violet and blue at the  
exterior ,limbs of each ,ring1 and the  
red and yellow at the interior4 ,and the
 violet1 by reason of the greatest      
obliquity of its ,rays1 being in        
proportion most of all expanded1 will   
soonest appear at the exterior ,limb of 
each white ,ring1 and become more       
conspicuous than the rest4 ,and the     
several ,series of ,colours belonging to
 the several ,rings1 will1 by their     
unfolding and spreading1 begin again to 
interfere1 and thereby render the ,rings
 less distinct1 and not visible to so   
great numbers4  ,if instead of the      
,prisms the ,object-glasses be made use 
of1 the ,rings which they exhibit become
 not white and distinct by the obliquity
 of the ,eye1 by reason that the ,rays  
in their passage through that ,air which
 intercedes the ,glasses are very nearly
 parallel to those ,lines in which they 
were first incident on the ,glasses1 and

 consequently the ,rays endued with     
several ,colours are not inclined one   
more than another to that ,air1 as it   
happens in the ,prisms4  ,there is yet  
another circumstance of these           
,experiments to be consider'd1 and that 
is why the black and white ,rings which 
when view'd at a distance appear        
distinct1 should not only become        
confused by viewing them near at hand1  
but also yield a violet ,colour at both 
the edges of every white ,ring4 ,and the
 reason is1 that the ,rays which enter  
the ,eye at several parts of the ,pupil1
 have several ,obliquities to the       
,glasses1 and those which are most      
oblique1 if consider'd apart1 would     
represent the ,rings bigger than those  
which are the least oblique4 ,whence the
 breadth of the ,perimeter of every     
white ,ring is expanded outwards by the 
obliquest ,rays1 and inwards by the     
least oblique4 ,and this ,expansion is  
so much the greater by how much the     
greater is the difference of the        

,obliquity2 that is1 by how much the    
,pupil is wider1 or the ,eye nearer to  
the ,glasses4 ,and the breadth of the   
violet must be most expanded1 because   
the ,rays apt to excite a ,sensation of 
that ,colour are most oblique to a      
second or farther ,superficies of the   
thinn'd ,air at which they are          
reflected1 and have also the greatest   
variation of ,obliquity1 which makes    
that ,colour soonest emerge out of the  
edges of the white4 ,and as the breadth 
of every ,ring is thus augmented1 the   
dark ,intervals must be diminish'd1     
until the neighbouring ,rings become    
continuous1 and are blended1 the        
exterior first1 and then those nearer   
the center2 so that they can no longer  
be distinguish'd apart1 but seem to     
constitute an even and uniform          
whiteness4  ,among all the ,observations
 there is none accompanied with so odd  
circumstances as the twenty-fourth4 ,of 
those the principal are1 that in thin   
,plates1 which to the naked ,eye seem of

 an even and uniform transparent        
whiteness1 without any terminations of  
,shadows1 the ,refraction of a ,prism   
should make ,rings of ,colours appear1  
whereas it usually makes ,objects appear
 colour'd only there where they are     
terminated with ,shadows1 or have parts 
unequally luminous2 and that it should  
make those ,rings exceedingly distinct  
and white1 although it usually renders  
,objects confused and coloured4 ,the    
,cause of these things you will         
understand by considering1 that all the 
,rings of ,colours are really in the    
,plate1 when view'd with the naked ,eye1
 although by reason of the great breadth
 of their ,circumferences they so much  
interfere and are blended together1 that
 they seem to constitute an uniform     
whiteness4 ,but when the ,rays pass     
through the ,prism to the ,eye1 the     
,orbits of the several ,colours in every
 ,ring are refracted1 some more than    
others1 according to their degrees of   
,refrangibility3 ,by which means the    

,colours on one side of the ,ring 7that 
is in the circumference on one side of  
its center71 become more unfolded and   
dilated1 and those on the other side    
more complicated and contracted4 ,and   
where by a due ,refraction they are so  
much contracted1 that the several ,rings
 become narrower than to interfere with 
one another1 they must appear distinct1 
and also white1 if the constituent      
,colours be so much contracted as to be 
wholly co-incident4 ,but on the other   
side1 where the ,orbit of every ,ring is
 made broader by the farther unfolding  
of its ,colours1 it must interfere more 
with other ,rings than before1 and so   
become less distinct4  ,illustration3   
,,fig4 #g4  ,to explain this a little   
farther1 suppose the concentrick        
,circles ,,av1 and ,,bx1 in ,fig4 #g4   
represent the red and violet of any     
,order1 which1 together with the        
intermediate ,colours1 constitute any   
one of these ,rings4 ,now these being   
view'd through a ,prism1 the violet     

,circle ,,bx1 will1 by a greater        
,refraction1 be farther translated from 
its place than the red ,,av1 and so     
approach nearer to it on that side of   
the ,circles1 towards which the         
,refractions are made4 ,for instance1 if
 the red be translated to av1 the violet
 may be translated to bx1 so as to      
approach nearer to it at x than before2 
and if the red be farther translated to 
av1 the violet may be so much farther   
translated to bx as to convene with it  
at x2 and if the red be yet farther     
translated to ,greek3 a,y1 the violet   
may be still so much farther translated 
to ,greek3 bx as to pass beyond it at   
,greek3 x1 and convene with it at e and 
f4 ,and this being understood not only  
of the red and violet1 but of all the   
other intermediate ,colours1 and also of
 every revolution of those ,colours1 you
 will easily perceive how those of the  
same revolution or order1 by their      
nearness at xv and ,greek3 ,yx1 and     
their coincidence at xv1 e and f1 ought 

to constitute pretty distinct ,arcs of  
,circles1 especially at xv1 or at e and 
f2 and that they will appear severally  
at x,greek3 u and at xv exhibit         
whiteness by their coincidence1 and     
again appear severally at ,greek3 ,yx1  
but yet in a contrary order to that     
which they had before1 and still retain 
beyond e and f4 ,but on the other side1 
at ab1 ab1 or ,greek3 ab1 these ,colours
 must become much more confused by being
 dilated and spread so as to interfere  
with those of other ,orders4 ,and the   
same confusion will happen at ,greek3   
,ux between e and f1 if the ,refraction 
be very great1 or the ,prism very       
distant from the ,object-glasses3 ,in   
which case no parts of the ,rings will  
be seen1 save only two little ,arcs at e
 and f1 whose distance from one another 
will be augmented by removing the ,prism
 still farther from the ,object-glasses3
 ,and these little ,arcs must be        
distinctest and whitest at their middle1
 and at their ends1 where they begin to 

grow confused1 they must be colour'd4   
,and the ,colours at one end of every   
,arc must be in a contrary order to     
those at the other end1 by reason that  
they cross in the intermediate white2   
namely1 their ends1 which verge towards 
,greek3 ,ux1 will be red and yellow on  
that side next the center1 and blue and 
violet on the other side4 ,but their    
other ends which verge from ,greek3 ,ux1
 will on the contrary be blue and violet
 on that side towards the center1 and on
 the other side red and yellow4  ,now as
 all these things follow from the       
properties of ,light by a mathematical  
way of reasoning1 so the truth of them  
may be manifested by ,experiments4 ,for 
in a dark ,room1 by viewing these ,rings
 through a ,prism1 by reflexion of the  
several prismatick ,colours1 which an   
assistant causes to move to and fro upon
 a ,wall or ,paper from whence they are 
reflected1 whilst the ,spectator's ,eye1
 the ,prism1 and the ,object-glasses1   
7as in the #acth ,observation17 are     

placed steady2 the ,position of the     
,circles made successively by the       
several ,colours1 will be found such1 in
 respect of one another1 as ,i have     
described in the ,figures abxv1 or abxv1
 or ,greek3 abx,u4 ,and by the same     
method the truth of the ,explications of
 other ,observations may be examined4   
,by what hath been said1 the like       
,phaenomena of ,water and thin ,plates  
of ,glass may be understood4 ,but in    
small fragments of those ,plates there  
is this farther observable1 that where  
they lie flat upon a ,table1 and are    
turned about their centers whilst they  
are view'd through a ,prism1 they will  
in some postures exhibit ,waves of      
various ,colours2 and some of them      
exhibit these ,waves in one or two      
,positions only1 but the most of them do
 in all ,positions exhibit them1 and    
make them for the most part appear      
almost all over the ,plates4 ,the reason
 is1 that the ,superficies of such      
,plates are not even1 but have many     

,cavities and ,swellings1 which1 how    
shallow soever1 do a little vary the    
thickness of the ,plate4 ,for at the    
several sides of those ,cavities1 for   
the ,reasons newly described1 there     
ought to be produced ,waves in several  
postures of the ,prism4 ,now though it  
be but some very small and narrower     
parts of the ,glass1 by which these     
,waves for the most part are caused1 yet
 they may seem to extend themselves over
 the whole ,glass1 because from the     
narrowest of those parts there are      
,colours of several ,orders1 that is1 of
 several ,rings1 confusedly reflected1  
which by ,refraction of the ,prism are  
unfolded1 separated1 and1 according to  
their degrees of ,refraction1 dispersed 
to several places1 so as to constitute  
so many several ,waves1 as there were   
divers orders of ,colours promiscuously 
reflected from that part of the ,glass4 
,these are the principal ,phaenomena of 
thin ,plates or ,bubbles1 whose         
,explications depend on the properties  

of ,light1 which ,i have heretofore     
deliver'd4 ,and these you see do        
necessarily follow from them1 and agree 
with them1 even to their very least     
circumstances2 and not only so1 but do  
very much tend to their proof4 ,thus1 by
 the #bdth ,observation it appears1 that
 the ,rays of several ,colours1 made as 
well by thin ,plates or ,bubbles1 as by 
,refractions of a ,prism1 have several  
degrees of ,refrangibility2 whereby     
those of each order1 which at the       
reflexion from the ,plate or ,bubble are
 intermix'd with those of other orders1 
are separated from them by ,refraction1 
and associated together so as to become 
visible by themselves like ,arcs of     
,circles4 ,for if the ,rays were all    
alike refrangible1 'tis impossible that 
the whiteness1 which to the naked ,sense
 appears uniform1 should by ,refraction 
have its parts transposed and ranged    
into those black and white ,arcs4  ,it  
appears also that the unequal           
,refractions of difform ,rays proceed   

not from any contingent irregularities2 
such as are ,veins1 an uneven ,polish1  
or fortuitous ,position of the ,pores of
 ,glass2 unequal and casual ,motions in 
the ,air or ,a,ether1 the spreading1    
breaking1 or dividing the same ,ray into
 many diverging parts2 or the like4     
,for1 admitting any such irregularities1
 it would be impossible for ,refractions
 to render those ,rings so very         
distinct1 and well defined1 as they do  
in the #bdth ,observation4 ,it is       
necessary therefore that every ,ray have
 its proper and constant degree of      
,refrangibility connate with it1        
according to which its refraction is    
ever justly and regularly perform'd2 and
 that several ,rays have several of     
those degrees4  ,and what is said of    
their ,refrangibility may be also       
understood of their ,reflexibility1 that
 is1 of their ,dispositions to be       
reflected1 some at a greater1 and others
 at a less thickness of thin ,plates or 
,bubbles2 namely1 that those            

,dispositions are also connate with the 
,rays1 and immutable2 as may appear by  
the #acth1 #adth1 and #aeth             
,observations1 compared with the fourth 
and eighteenth4  ,by the ,precedent     
,observations it appears also1 that     
whiteness is a dissimilar mixture of all
 ,colours1 and that ,light is a mixture 
of ,rays endued with all those ,colours4
 ,for1 considering the multitude of the 
,rings of ,colours in the #c;d1 #abth1  
and #bdth ,observations1 it is manifest1
 that although in the #dth and #ahth    
,observations there appear no more than 
eight or nine of those ,rings1 yet there
 are really a far greater number1 which 
so much interfere and mingle with one   
another1 as after those eight or nine   
revolutions to dilute one another       
wholly1 and constitute an even and      
sensibly uniform whiteness4 ,and        
consequently that whiteness must be     
allow'd a mixture of all ,colours1 and  
the ,light which conveys it to the ,eye 
must be a mixture of ,rays endued with  

all those ,colours4  ,but farther2 by   
the #bdth ,observation it appears1 that 
there is a constant relation between    
,colours and ,refrangibility2 the most  
refrangible ,rays being violet1 the     
least refrangible red1 and those of     
intermediate ,colours having            
proportionably intermediate degrees of  
,refrangibility4 ,and by the #acth1     
#adth1 and #aeth ,observations1 compared
 with the #dth or #ahth there appears to
 be the same constant relation between  
,colour and ,reflexibility2 the violet  
being in like circumstances reflected at
 least thicknesses of any thin ,plate or
 ,bubble1 the red at greatest           
thicknesses1 and the intermediate       
,colours at intermediate thicknesses4   
,whence it follows1 that the colorifick 
,dispositions of ,rays are also connate 
with them1 and immutable2 and by        
consequence1 that all the ,productions  
and ,appearances of ,colours in the     
,world are derived1 not from any        
physical ,change caused in ,light by    

,refraction or ,reflexion1 but only from
 the various ,mixtures or ,separations  
of ,rays1 by virtue of their different  
,refrangibility or ,reflexibility4 ,and 
in this respect the ,science of ,colours
 becomes a ,speculation as truly        
mathematical as any other part of       
,opticks4 ,i mean1 so far as they depend
 on the ,nature of ,light1 and are not  
produced or alter'd by the ,power of    
,imagination1 or by striking or pressing
 the ,eye4     ,,the  ,,second ,,book   
,,of  ,,opticks   ,,part ,,iii4  ,of the
 permanent ,colours of natural ,bodies1 
and the ,analogy between them and the   
,colours of thin transparent ,plates4   
,i am now come to another part of this  
,design1 which is to consider how the   
,phaenomena of thin transparent ,plates 
stand related to those of all other     
natural ,bodies4 ,of these ,bodies ,i   
have already told you that they appear  
of divers ,colours1 accordingly as they 
are disposed to reflect most copiously  
the ,rays originally endued with those  

,colours4 ,but their ,constitutions1    
whereby they reflect some ,rays more    
copiously than others1 remain to be     
discover'd2 and these ,i shall endeavour
 to manifest in the following           
,propositions4   ,,prop4 ,i4  ,those    
,superficies of transparent ,bodies     
reflect the greatest quantity of ,light1
 which have the greatest refracting     
,power2 that is1 which intercede        
,mediums that differ most in their      
refractive ,densities4 ,and in the      
,confines of equally refracting ,mediums
 there is no ,reflexion4  ,the ,analogy 
between ,reflexion and ,refraction will 
appear by considering1 that when ,light 
passeth obliquely out of one ,medium    
into another which refracts from the    
perpendicular1 the greater is the       
difference of their refractive ,density1
 the less ,obliquity of ,incidence is   
requisite to cause a total ,reflexion4  
,for as the ,sines are which measure the
 ,refraction1 so is the ,sine of        
,incidence at which the total ,reflexion

 begins1 to the ,radius of the ,circle2 
and consequently that ,angle of         
,incidence is least where there is the  
greatest difference of the ,sines4 ,thus
 in the passing of ,light out of ,water 
into ,air1 where the ,refraction is     
measured by the ,ratio of the ,sines #c 
to #d1 the total ,reflexion begins when 
the ,angle of ,incidence is about #dh   
,degrees #ce ,minutes4 ,in passing out  
of ,glass into ,air1 where the          
,refraction is measured by the ,ratio of
 the ,sines #bj to #ca1 the total       
,reflexion begins when the ,angle of    
,incidence is #dj ,degrees #aj ,minutes2
 and so in passing out of ,crystal1 or  
more strongly refracting ,mediums into  
,air1 there is still a less obliquity   
requisite to cause a total reflexion4   
,superficies therefore which refract    
most do soonest reflect all the ,light  
which is incident on them1 and so must  
be allowed most strongly reflexive4     
,but the truth of this ,proposition will
 farther appear by observing1 that in   

the ,superficies interceding two        
transparent ,mediums1 7such as are ,air1
 ,water1 ,oil1 common ,glass1 ,crystal1 
metalline ,glasses1 ,island ,glasses1   
white transparent ,arsenick1 ,diamonds1 
c47 the ,reflexion is stronger or weaker
 accordingly1 as the ,superficies hath a
 greater or less refracting ,power4 ,for
 in the ,confine of ,air and ,sal-gem   
'tis stronger than in the ,confine of   
,air and ,water1 and still stronger in  
the ,confine of ,air and common ,glass  
or ,crystal1 and stronger in the        
,confine of ,air and a ,diamond4 ,if any
 of these1 and such like transparent    
,solids1 be immerged in ,water1 its     
,reflexion becomes1 much weaker than    
before2 and still weaker if they be     
immerged in the more strongly refracting
 ,liquors of well rectified ,oil of     
,vitriol or ,spirit of ,turpentine4 ,if 
,water be distinguish'd into two parts  
by any imaginary ,surface1 the          
,reflexion in the ,confine of those two 
parts is none at all4 ,in the ,confine  

of ,water and ,ice 'tis very little2 in 
that of ,water and ,oil 'tis something  
greater2 in that of ,water and ,sal-gem 
still greater2 and in that of ,water and
 ,glass1 or ,crystal or other denser    
,substances still greater1 accordingly  
as those ,mediums differ more or less in
 their refracting ,powers4 ,hence in the
 ,confine of common ,glass and ,crystal1
 there ought to be a weak ,reflexion1   
and a stronger ,reflexion in the        
,confine of common and metalline ,glass2
 though ,i have not yet tried this4 ,but
 in the ,confine of two ,glasses of     
equal density1 there is not any sensible
 ,reflexion2 as was shewn in the first  
,observation4 ,and the same may be      
understood of the ,superficies          
interceding two ,crystals1 or two       
,liquors1 or any other ,substances in   
which no ,refraction is caused4 ,so then
 the reason why uniform pellucid        
,mediums 7such as ,water1 ,glass1 or    
,crystal17 have no sensible ,reflexion  
but in their external ,superficies1     

where they are adjacent to other        
,mediums of a different density1 is     
because all their contiguous parts have 
one and the same degree of density4     
,,prop4 ,,ii4  ,the least parts of      
almost all natural ,bodies are in some  
measure transparent3 ,and the ,opacity  
of those ,bodies ariseth from the       
multitude of ,reflexions caused in their
 internal ,parts4  ,that this is so has 
been observed by others1 and will easily
 be granted by them that have been      
conversant with ,microscopes4 ,and it   
may be also tried by applying any       
substance to a hole through which some  
,light is immitted into a dark ,room4   
,for how opake soever that ,substance   
may seem in the open ,air1 it will by   
that means appear very manifestly       
transparent1 if it be of a sufficient   
thinness4 ,only white metalline ,bodies 
must be excepted1 which by reason of    
their excessive density seem to reflect 
almost all the ,light incident on their 
first ,superficies2 unless by solution  

in ,menstruums they be reduced into very
 small ,particles1 and then they become 
transparent4   ,,prop4 ,,iii4  ,between 
the parts of opake and colour'd ,bodies 
are many ,spaces1 either empty1 or      
replenish'd with ,mediums of other      
,densities2 as ,water between the       
tinging ,corpuscles wherewith any       
,liquor is impregnated1 ,air between the
 aqueous ,globules that constitute      
,clouds or ,mists2 and for the most part
 ,spaces void of both ,air and ,water1  
but yet perhaps not wholly void of all  
,substance1 between the parts of hard   
,bodies4  ,the truth of this is evinced 
by the two precedent ,propositions3 ,for
 by the second ,proposition there are   
many ,reflexions made by the internal   
parts of ,bodies1 which1 by the first   
,proposition1 would not happen if the   
parts of those ,bodies were continued   
without any such ,interstices between   
them2 because ,reflexions are caused    
only in ,superficies1 which intercede   
,mediums of a differing density1 by     

,prop4 #a4  ,but farther1 that this     
discontinuity of parts is the principal 
,cause of the opacity of ,bodies1 will  
appear by considering1 that opake       
,substances become transparent by       
filling their ,pores with any ,substance
 of equal or almost equal density with  
their parts4 ,thus ,paper dipped in     
,water or ,oil1 the ,oculus ,mundi      
,stone steep'd in ,water1 ,linnen ,cloth
 oiled or varnish'd1 and many other     
,substances soaked in such ,liquors as  
will intimately pervade their little    
,pores1 become by that means more       
transparent than otherwise2 so1 on the  
contrary1 the most transparent          
,substances1 may1 by evacuating their   
,pores1 or separating their parts1 be   
render'd sufficiently opake2 as ,salts  
or wet ,paper1 or the ,oculus ,mundi    
,stone by being dried1 ,horn by being   
scraped1 ,glass by being reduced to     
,powder1 or otherwise flawed2           
,turpentine by being stirred about with 
,water till they mix imperfectly1 and   

,water by being form'd into many small  
,bubbles1 either alone in the form of   
,froth1 or by shaking it together with  
,oil of ,turpentine1 or ,oil ,olive1 or 
with some other convenient ,liquor1 with
 which it will not perfectly            
incorporate4 ,and to the increase of the
 opacity of these ,bodies1 it conduces  
something1 that by the #bc;d            
,observation the ,reflexions of very    
thin transparent ,substances are        
considerably stronger than those made by
 the same ,substances of a greater      
thickness4   ,,prop4 ,,iv4  ,the ,parts 
of ,bodies and their ,interstices must  
not be less than of some definite       
bigness1 to render them opake and       
colour'd4  ,for the opakest ,bodies1 if 
their parts be subtilly divided1 7as    
,metals1 by being dissolved in acid     
,menstruums1 c47 become perfectly       
transparent4 ,and you may also remember1
 that in the eighth ,observation there  
was no sensible reflexion at the        
,superficies of the ,object-glasses1    

where they were very near one another1  
though they did not absolutely touch4   
,and in the #agth ,observation the      
,reflexion of the ,water-bubble where it
 became thinnest was almost insensible1 
so as to cause very black ,spots to     
appear on the top of the ,bubble1 by the
 want of reflected ,light4  ,on these   
grounds ,i perceive it is that ,water1  
,salt1 ,glass1 ,stones1 and such like   
,substances1 are transparent4 ,for1 upon
 divers ,considerations1 they seem to be
 as full of ,pores or ,interstices      
between their parts as other ,bodies    
are1 but yet their ,parts and           
,interstices to be too small to cause   
,reflexions in their common ,surfaces4  
,,prop4 ,v4  ,the transparent parts of  
,bodies1 according to their several     
sizes1 reflect ,rays of one ,colour1 and
 transmit those of another1 on the same 
grounds that thin ,plates or ,bubbles do
 reflect or transmit those ,rays4 ,and  
this ,i take to be the ground of all    
their ,colours4  ,for if a thinn'd or   

plated ,body1 which being of an even    
thickness1 appears all over of one      
uniform ,colour1 should be slit into    
,threads1 or broken into ,fragments1 of 
the same thickness with the ,plate2 ,i  
see no reason why every ,thread or      
,fragment should not keep its ,colour1  
and by consequence why a heap of those  
,threads or ,fragments should not       
constitute a ,mass or ,powder of the    
same ,colour1 which the ,plate exhibited
 before it was broken4 ,and the parts of
 all natural ,bodies being like so many 
,fragments of a ,plate1 must on the same
 grounds exhibit the same ,colours4     
,now1 that they do so will appear by the
 affinity of their ,properties4 ,the    
finely colour'd ,feathers of some       
,birds1 and particularly those of       
,peacocks ,tails1 do1 in the very same  
part of the ,feather1 appear of several 
,colours in several ,positions of the   
,eye1 after the very same manner that   
thin ,plates were found to do in the    
#gth and #aith ,observations1 and       

therefore their ,colours arise from the 
thinness of the transparent parts of the
 ,feathers2 that is1 from the           
slenderness of the very fine ,hairs1 or 
,capillamenta1 which grow out of the    
sides of the grosser lateral ,branches  
or ,fibres of those ,feathers4 ,and to  
the same purpose it is1 that the ,webs  
of some ,spiders1 by being spun very    
fine1 have appeared colour'd1 as some   
have observ'd1 and that the colour'd    
,fibres of some ,silks1 by varying the  
,position of the ,eye1 do vary their    
,colour4 ,also the ,colours of ,silks1  
,cloths1 and other ,substances1 which   
,water or ,oil can intimately penetrate1
 become more faint and obscure by being 
immerged in those ,liquors1 and recover 
their ,vigor again by being dried2 much 
after the manner declared of thin       
,bodies in the #ajth and #bast          
,observations4 ,leaf-,gold1 some sorts  
of painted ,glass1 the ,infusion of     
,lignum ,nephriticum1 and some other    
,substances1 reflect one ,colour1 and   

transmit another2 like thin ,bodies in  
the #ith and #bjth ,observations4 ,and  
some of those colour'd ,powders which   
,painters use1 may have their ,colours a
 little changed1 by being very          
elaborately and finely ground4 ,where ,i
 see not what can be justly pretended   
for those changes1 besides the breaking 
of their parts into less parts by that  
contrition1 after the same manner that  
the ,colour of a thin ,plate is changed 
by varying its thickness4 ,for which    
reason also it is that the colour'd     
,flowers of ,plants and ,vegetables1 by 
being bruised1 usually become more      
transparent than before1 or at least in 
some degree or other change their       
,colours4 ,nor is it much less to my    
purpose1 that1 by mixing divers         
,liquors1 very odd and remarkable       
,productions and ,changes of ,colours   
may be effected1 of which no cause can  
be more obvious and rational than that  
the saline ,corpuscles of one ,liquor do
 variously act upon or unite with the   

tinging ,corpuscles of another1 so as to
 make them swell1 or shrink1 7whereby   
not only their bulk but their density   
also may be changed17 or to divide them 
into smaller ,corpuscles1 7whereby a    
colour'd ,liquor may become             
transparent17 or to make many of them   
associate into one cluster1 whereby two 
transparent ,liquors may compose a      
colour'd one4 ,for we see how apt those 
saline ,menstruums are to penetrate and 
dissolve ,substances to which they are  
applied1 and some of them to precipitate
 what others dissolve4 ,in like manner1 
if we consider the various ,phaenomena  
of the ,atmosphere1 we may observe1 that
 when ,vapours are first raised1 they   
hinder not the transparency of the ,air1
 being divided into parts too small to  
cause any ,reflexion in their           
,superficies4 ,but when in order to     
compose drops of ,rain they begin to    
coalesce and constitute ,globules of all
 intermediate sizes1 those ,globules1   
when they become of convenient size to  

reflect some ,colours and transmit      
others1 may constitute ,clouds of       
various ,colours according to their     
sizes4 ,and ,i see not what can be      
rationally conceived in so transparent a
 ,substance as ,water for the production
 of these ,colours1 besides the various 
sizes of its fluid and globular         
,parcels4   ,,prop4 ,,vi4  ,the parts of
 ,bodies on which their ,colours depend1
 are denser than the ,medium which      
pervades their ,interstices4  ,this will
 appear by considering1 that the ,colour
 of a ,body depends not only on the     
,rays which are incident perpendicularly
 on its parts1 but on those also which  
are incident at all other ,angles4 ,and 
that according to the #gth ,observation1
 a very little variation of obliquity   
will change the reflected ,colour1 where
 the thin ,body or small ,particles is  
rarer than the ambient ,medium1 insomuch
 that such a small ,particle will at    
diversly oblique ,incidences reflect all
 sorts of ,colours1 in so great a       

variety that the ,colour resulting from 
them all1 confusedly reflected from a   
heap of such ,particles1 must rather be 
a white or grey than any other ,colour1 
or at best it must be but a very        
imperfect and dirty ,colour4 ,whereas if
 the thin ,body or small ,particle be   
much denser than the ambient ,medium1   
the ,colours1 according to the #aith    
,observation1 are so little changed by  
the variation of obliquity1 that the    
,rays which are reflected least         
obliquely may predominate over the rest1
 so much as to cause a heap of such     
,particles to appear very intensely of  
their ,colour4  ,it conduces also       
something to the confirmation of this   
,proposition1 that1 according to the    
#bb;d ,observation1 the ,colours        
exhibited by the denser thin ,body      
within the rarer1 are more brisk than   
those exhibited by the rarer within the 
denser4   ,,prop4 ,,vii4  ,the bigness  
of the component parts of natural       
,bodies may be conjectured by their     

,colours4  ,for since the parts of these
 ,bodies1 by ,prop4 #e4 do most probably
 exhibit the same ,colours with a ,plate
 of equal thickness1 provided they have 
the same refractive density2 and since  
their parts seem for the most part to   
have much the same density with ,water  
or ,glass1 as by many circumstances is  
obvious to collect2 to determine the    
sizes of those parts1 you need only have
 recourse to the precedent ,tables1 in  
which the thickness of ,water or ,glass 
exhibiting any ,colour is expressed4    
,thus if it be desired to know the      
diameter of a ,corpuscle1 which being of
 equal density with ,glass shall reflect
 green of the third ,order2 the ,number 
#af-a_/d shews it to be                 
7#af-a_/d7_/ajjjj parts of an ,inch4    
,the greatest difficulty is here to know
 of what ,order the ,colour of any ,body
 is4 ,and for this end we must have     
recourse to the #dth and #ahth          
,observations2 from whence may be       
collected these particulars4  ,scarlets1

 and other reds1 oranges1 and yellows1  
if they be pure and intense1 are most   
probably of the second order4 ,those of 
the first and third order also may be   
pretty good2 only the yellow of the     
first order is faint1 and the orange and
 red of the third ,order have a great   
,mixture of violet and blue4  ,there may
 be good ,greens of the fourth ,order1  
but the purest are of the third4 ,and of
 this ,order the green of all           
,vegetables seems to be1 partly by      
reason of the ,intenseness of their     
,colours1 and partly because when they  
wither some of them turn to a greenish  
yellow1 and others to a more perfect    
yellow or orange1 or perhaps to red1    
passing first through all the aforesaid 
intermediate ,colours4 ,which ,changes  
seem to be effected by the exhaling of  
the ,moisture which may leave the       
tinging ,corpuscles more dense1 and     
something augmented by the ,accretion of
 the oily and earthy ,part of that      
,moisture4 ,now the green1 without      

doubt1 is of the same ,order with those 
,colours into which it changeth1 because
 the ,changes are gradual1 and those    
,colours1 though usually not very full1 
yet are often too full and lively to be 
of the fourth ,order4  ,blues and       
,purples may be either of the second or 
third ,order1 but the best are of the   
third4 ,thus the ,colour of ,violets    
seems to be of that ,order1 because     
their ,syrup by acid ,liquors turns red1
 and by urinous and alcalizate turns    
green4 ,for since it is of the ,nature  
of ,acids to dissolve or attenuate1 and 
of ,alcalies to precipitate or          
incrassate1 if the ,purple ,colour of   
the ,syrup was of the second ,order1 an 
acid ,liquor by attenuating its tinging 
,corpuscles would change it to a red of 
the first ,order1 and an ,alcali by     
incrassating them would change it to a  
green of the second ,order2 which red   
and green1 especially the green1 seem   
too imperfect to be the ,colours        
produced by these ,changes4 ,but if the 

said ,purple be supposed of the third   
,order1 its ,change to red of the       
second1 and green of the third1 may     
without any ,inconvenience be allow'd4  
,if there be found any ,body of a deeper
 and less reddish ,purple than that of  
the ,violets1 its ,colour most probably 
is of the second ,order4 ,but yet there 
being no ,body commonly known whose     
,colour is constantly more deep than    
theirs1 ,i have made use of their ,name 
to denote the deepest and least reddish 
,purples1 such as manifestly transcend  
their ,colour in purity4  ,the blue of  
the first ,order1 though very faint and 
little1 may possibly be the ,colour of  
some ,substances2 and particularly the  
azure ,colour of the ,skies seems to be 
of this ,order4 ,for all ,vapours when  
they begin to condense and coalesce into
 small ,parcels1 become first of that   
,bigness1 whereby such an ,azure must be
 reflected before they can constitute   
,clouds of other ,colours4 ,and so this 
being the first ,colour which ,vapours  

begin to reflect1 it ought to be the    
,colour of the finest and most          
transparent ,skies1 in which ,vapours   
are not arrived to that ,grossness      
requisite to reflect other ,colours1 as 
we find it is by ,experience4           
,whiteness1 if most intense and         
luminous1 is that of the first ,order1  
if less strong and luminous1 a ,mixture 
of the ,colours of several ,orders4 ,of 
this last kind is the ,whiteness of     
,froth1 ,paper1 ,linnen1 and most white 
,substances2 of the former ,i reckon    
that of white ,metals to be4 ,for whilst
 the densest of ,metals1 ,gold1 if      
foliated1 is transparent1 and all       
,metals become transparent if dissolved 
in ,menstruums or vitrified1 the        
,opacity of white ,metals ariseth not   
from their ,density alone4 ,they being  
less dense than ,gold would be more     
transparent than it1 did not some other 
,cause concur with their ,density to    
make them opake4 ,and this ,cause ,i    
take to be such a ,bigness of their     

,particles as fits them to reflect the  
white of the first order4 ,for1 if they 
be of other ,thicknesses they may       
reflect other ,colours1 as is manifest  
by the ,colours which appear upon hot   
,steel in tempering it1 and sometimes   
upon the ,surface of melted ,metals in  
the ,skin or ,scoria which arises upon  
them in their cooling4 ,and as the white
 of the first order is the strongest    
which can be made by ,plates of         
transparent ,substances1 so it ought to 
be stronger in the denser ,substances of
 ,metals than in the rarer of ,air1     
,water1 and ,glass4 ,nor do ,i see but  
that metallick ,substances of such a    
,thickness as may fit them to reflect   
the white of the first order1 may1 by   
reason of their great ,density          
7according to the ,tenor of the first of
 these ,propositions7 reflect all the   
,light incident upon them1 and so be as 
opake and splendent as it's possible for
 any ,body to be4 ,gold1 or ,copper     
mix'd with less than half their ,weight 

of ,silver1 or ,tin1 or ,regulus of     
,antimony1 in fusion1 or amalgamed with 
a very little ,mercury1 become white2   
which shews both that the ,particles of 
white ,metals have much more            
,superficies1 and so are smaller1 than  
those of ,gold and ,copper1 and also    
that they are so opake as not to suffer 
the ,particles of ,gold or ,copper to   
shine through them4 ,now it is scarce to
 be doubted but that the ,colours of    
,gold and ,copper are of the second and 
third order1 and therefore the          
,particles of white ,metals cannot be   
much bigger than is requisite to make   
them reflect the white of the first     
order4 ,the ,volatility of ,mercury     
argues that they are not much bigger1   
nor may they be much less1 lest they    
lose their ,opacity1 and become either  
transparent as they do when attenuated  
by ,vitrification1 or by ,solution in   
,menstruums1 or black as they do when   
ground smaller1 by rubbing ,silver1 or  
,tin1 or ,lead1 upon other ,substances  

to draw black ,lines4 ,the first and    
only ,colour which white ,metals take by
 grinding their ,particles smaller1 is  
black1 and therefore their white ought  
to be that which borders upon the black 
,spot in the ,center of the ,rings of   
,colours1 that is1 the white of the     
first order4 ,but1 if you would hence   
gather the ,bigness of metallick        
,particles1 you must allow for their    
,density4 ,for were ,mercury            
transparent1 its ,density is such that  
the ,sine of ,incidence upon it 7by my  
,computation7 would be to the ,sine of  
its ,refraction1 as #ga to #bj1 or #g to
 #b4 ,and therefore the ,thickness of   
its ,particles1 that they may exhibit   
the same ,colours with those of ,bubbles
 of ,water1 ought to be less than the   
,thickness of the ,skin of those        
,bubbles in the ,proportion of #b to #g4
 ,whence it's possible1 that the        
,particles of ,mercury may be as little 
as the ,particles of some transparent   
and volatile ,fluids1 and yet reflect   

the white of the first order4  ,lastly1 
for the production of black1 the        
,corpuscles must be less than any of    
those which exhibit ,colours4 ,for at   
all greater sizes there is too much     
,light reflected to constitute this     
,colour4 ,but if they be supposed a     
little less than is requisite to reflect
 the white and very faint blue of the   
first order1 they will1 according to the
 #dth1 #hth1 #agth and #ahth            
,observations1 reflect so very little   
,light as to appear intensely black1 and
 yet may perhaps variously refract it to
 and fro within themselves so long1     
until it happen to be stifled and lost1 
by which means they will appear black in
 all positions of the ,eye without any  
transparency4 ,and from hence may be    
understood why ,fire1 and the more      
subtile dissolver ,putrefaction1 by     
dividing the ,particles of ,substances1 
turn them to black1 why small quantities
 of black ,substances impart their      
,colour very freely and intensely to    

other ,substances to which they are     
applied2 the minute ,particles of these1
 by reason of their very great number1  
easily overspreading the gross          
,particles of others2 why ,glass ground 
very elaborately with ,sand on a ,copper
 ,plate1 'till it be well polish'd1     
makes the ,sand1 together with what is  
worn off from the ,glass and ,copper1   
become very black3 why black ,substances
 do soonest of all others become hot in 
the ,sun's ,light and burn1 7which      
,effect may proceed partly from the     
multitude of ,refractions in a little   
room1 and partly from the easy          
,commotion of so very small             
,corpuscles27 and why blacks are usually
 a little inclined to a bluish ,colour4 
,for that they are so may be seen by    
illuminating white ,paper by ,light     
reflected from black ,substances4 ,for  
the ,paper will usually appear of a     
bluish white2 and the reason is1 that   
black borders in the obscure blue of the
 order described in the #ahth           

,observation1 and therefore reflects    
more ,rays of that ,colour than of any  
other4  ,in these ,descriptions ,i have 
been the more particular1 because it is 
not impossible but that ,microscopes may
 at length be improved to the discovery 
of the ,particles of ,bodies on which   
their ,colours depend1 if they are not  
already in some measure arrived to that 
degree of perfection4 ,for if those     
,instruments are or can be so far       
improved as with sufficient distinctness
 to represent ,objects five or six      
hundred times bigger than at a ,foot    
distance they appear to our naked ,eyes1
 ,i should hope that we might be able to
 discover some of the greatest of those 
,corpuscles4 ,and by one that would     
magnify three or four thousand times    
perhaps they might all be discover'd1   
but those which produce blackness4 ,in  
the mean while ,i see nothing material  
in this ,discourse that may rationally  
be doubted of1 excepting this ,position3
 ,that transparent ,corpuscles of the   

same thickness and density with a       
,plate1 do exhibit the same ,colour4    
,and this ,i would have understood not  
without some ,latitude1 as well because 
those ,corpuscles may be of irregular   
,figures1 and many ,rays must be        
obliquely incident on them1 and so have 
a shorter way through them than the     
length of their ,diameters1 as because  
the straitness of the ,medium put in on 
all sides within such ,corpuscles may a 
little alter its ,motions or other      
qualities on which the ,reflexion       
depends4 ,but yet ,i cannot much suspect
 the last1 because ,i have observed of  
some small ,plates of ,muscovy ,glass   
which were of an even thickness1 that   
through a ,microscope they have appeared
 of the same ,colour at their edges and 
corners where the included ,medium was  
terminated1 which they appeared of in   
other places4 ,however it will add much 
to our ,satisfaction1 if those          
,corpuscles can be discover'd with      
,microscopes2 which if we shall at      

length attain to1 ,i fear it will be the
 utmost improvement of this ,sense4 ,for
 it seems impossible to see the more    
secret and noble ,works of ,nature      
within the ,corpuscles by reason of     
their transparency4   ,,prop4 ,,viii4   
,the ,cause of ,reflexion is not the    
impinging of ,light on the solid or     
impervious parts of ,bodies1 as is      
commonly believed4  ,this will appear by
 the following ,considerations4 ,first1 
,that in the passage of ,light out of   
,glass into ,air there is a ,reflexion  
as strong as in its passage out of ,air 
into ,glass1 or rather a little         
stronger1 and by many degrees stronger  
than in its passage out of ,glass into  
,water4 ,and it seems not probable that 
,air should have more strongly          
reflecting parts than ,water or ,glass4 
,but if that should possibly be         
supposed1 yet it will avail nothing2 for
 the ,reflexion is as strong or stronger
 when the ,air is drawn away from the   
,glass1 7suppose by the ,air-,pump      

invented by ,otto ,gueriet1 and improved
 and made useful by ,mr4 ,boyle7 as when
 it is adjacent to it4 ,secondly1 ,if   
,light in its passage out of ,glass into
 ,air be incident more obliquely than at
 an ,angle of #dj or #da ,degrees it is 
wholly reflected1 if less obliquely it  
is in great measure transmitted4 ,now it
 is not to be imagined that ,light at   
one degree of obliquity should meet with
 ,pores enough in the ,air to transmit  
the greater part of it1 and at another  
degree of obliquity should meet with    
nothing but parts to reflect it wholly1 
especially considering that in its      
passage out of ,air into ,glass1 how    
oblique soever be its ,incidence1 it    
finds ,pores enough in the ,glass to    
transmit a great part of it4 ,if any    
,man suppose that it is not reflected by
 the ,air1 but by the outmost           
superficial parts of the ,glass1 there  
is still the same difficulty3 ,besides1 
that such a ,supposition is             
unintelligible1 and will also appear to 

be false by applying ,water behind some 
part of the ,glass instead of ,air4 ,for
 so in a convenient obliquity of the    
,rays1 suppose of #de or #df ,degrees1  
at which they are all reflected where   
the ,air is adjacent to the ,glass1 they
 shall be in great measure transmitted  
where the ,water is adjacent to it2     
which argues1 that their ,reflexion or  
,transmission depends on the            
constitution of the ,air and ,water     
behind the ,glass1 and not on the       
striking of the ,rays upon the parts of 
the ,glass4 ,thirdly1 ,if the ,colours  
made by a ,prism placed at the entrance 
of a ,beam of ,light into a darken'd    
,room be successively cast on a second  
,prism placed at a greater distance from
 the former1 in such manner that they   
are all alike incident upon it1 the     
second ,prism may be so inclined to the 
incident ,rays1 that those which are of 
a blue ,colour shall be all reflected by
 it1 and yet those of a red ,colour     
pretty copiously transmitted4 ,now if   

the ,reflexion be caused by the parts of
 ,air or ,glass1 ,i would ask1 why at   
the same ,obliquity of ,incidence the   
blue should wholly impinge on those     
parts1 so as to be all reflected1 and   
yet the red find ,pores enough to be in 
a great measure transmitted4 ,fourthly1 
,where two ,glasses touch one another1  
there is no sensible ,reflexion1 as was 
declared in the first ,observation2 and 
yet ,i see no reason why the ,rays      
should not impinge on the parts of      
,glass1 as much when contiguous to other
 ,glass as when contiguous to ,air4     
,fifthly1 ,when the top of a            
,water-,bubble 7in the #agth            
,observation17 by the continual         
subsiding and exhaling of the ,water    
grew very thin1 there was such a little 
and almost insensible quantity of ,light
 reflected from it1 that it appeared    
intensely black2 whereas round about    
that black ,spot1 where the ,water was  
thicker1 the ,reflexion was so strong as
 to make the ,water seem very white4    

,nor is it only at the least thickness  
of thin ,plates or ,bubbles1 that there 
is no manifest ,reflexion1 but at many  
other thicknesses continually greater   
and greater4 ,for in the #aeth          
,observation the ,rays of the same      
,colour were by turns transmitted at one
 thickness1 and reflected at another    
thickness1 for an indeterminate number  
of ,successions4 ,and yet in the        
,superficies of the thinned ,body1 where
 it is of any one thickness1 there are  
as many parts for the ,rays to impinge  
on1 as where it is of any other         
thickness4 ,sixthly1 ,if ,reflexion were
 caused by the parts of reflecting      
,bodies1 it would be impossible for thin
 ,plates or ,bubbles1 at one and the    
same place1 to reflect the ,rays of one 
,colour1 and transmit those of another1 
as they do according to the #acth and   
#aeth ,observations4 ,for it is not to  
be imagined that at one place the ,rays 
which1 for instance1 exhibit a blue     
,colour1 should have the fortune to dash

 upon the parts1 and those which exhibit
 a red to hit upon the ,pores of the    
,body2 and then at another place1 where 
the ,body is either a little thicker or 
a little thinner1 that on the contrary  
the blue should hit upon its pores1 and 
the red upon its parts4 ,lastly1 ,were  
the ,rays of ,light reflected by        
impinging on the solid parts of ,bodies1
 their ,reflexions from polish'd ,bodies
 could not be so regular as they are4   
,for in polishing ,glass with ,sand1    
,putty1 or ,tripoly1 it is not to be    
imagined that those ,substances can1 by 
grating and fretting the ,glass1 bring  
all its least ,particles to an accurate 
,polish2 so that all their ,surfaces    
shall be truly plain or truly spherical1
 and look all the same way1 so as       
together to compose one even ,surface4  
,the smaller the ,particles of those    
,substances are1 the smaller will be the
 ,scratches by which they continually   
fret and wear away the ,glass until it  
be polish'd2 but be they never so small 

they can wear away the ,glass no        
otherwise than by grating and scratching
 it1 and breaking the ,protuberances2   
and therefore polish it no otherwise    
than by bringing its roughness to a very
 fine ,grain1 so that the ,scratches and
 ,frettings of the ,surface become too  
small to be visible4 ,and therefore if  
,light were reflected by impinging upon 
the solid parts of the ,glass1 it would 
be scatter'd as much by the most        
polish'd ,glass as by the roughest4 ,so 
then it remains a ,problem1 how ,glass  
polish'd by fretting ,substances can    
reflect ,light so regularly as it does4 
,and this ,problem is scarce otherwise  
to be solved1 than by saying1 that the  
,reflexion of a ,ray is effected1 not by
 a single point of the reflecting ,body1
 but by some power of the ,body which is
 evenly diffused all over its ,surface1 
and by which it acts upon the ,ray      
without immediate ,contact4 ,for that   
the parts of ,bodies do act upon ,light 
at a distance shall be shewn hereafter4 

,now if ,light be reflected1 not by     
impinging on the solid parts of ,bodies1
 but by some other principle2 it's      
probable that as many of its ,rays as   
impinge on the solid parts of ,bodies   
are not reflected but stifled and lost  
in the ,bodies4 ,for otherwise we must  
allow two sorts of ,reflexions4 ,should 
all the ,rays be reflected which impinge
 on the internal parts of clear ,water  
or ,crystal1 those ,substances would    
rather have a cloudy ,colour than a     
clear ,transparency4 ,to make ,bodies   
look black1 it's necessary that many    
,rays be stopp'd1 retained1 and lost in 
them2 and it seems not probable that any
 ,rays can be stopp'd and stifled in    
them which do not impinge on their      
parts4  ,and hence we may understand    
that ,bodies are much more rare and     
porous than is commonly believed4 ,water
 is nineteen times lighter1 and by      
consequence nineteen times rarer than   
,gold2 and ,gold is so rare as very     
readily and without the least opposition

 to transmit the magnetick ,effluvia1   
and easily to admit ,quicksilver into   
its ,pores1 and to let ,water pass      
through it4 ,for a concave ,sphere of   
,gold filled with ,water1 and solder'd  
up1 has1 upon pressing the ,sphere with 
great force1 let the ,water squeeze     
through it1 and stand all over its      
outside in multitudes of small ,drops1  
like ,dew1 without bursting or cracking 
the ,body of the ,gold1 as ,i have been 
inform'd by an ,eye witness4 ,from all  
which we may conclude1 that ,gold has   
more ,pores than solid parts1 and by    
consequence that ,water has above forty 
times more ,pores than ,parts4 ,and he  
that shall find out an ,hypothesis1 by  
which ,water may be so rare1 and yet not
 be capable of compression by force1 may
 doubtless by the same ,hypothesis make 
,gold1 and ,water1 and all other        
,bodies1 as much rarer as he pleases2 so
 that ,light may find a ready passage   
through transparent ,substances4  ,the  
,magnet acts upon ,iron through all     

dense ,bodies not magnetick nor red hot1
 without any diminution of its ,virtue2 
as for instance1 through ,gold1 ,silver1
 ,lead1 ,glass1 ,water4 ,the gravitating
 ,power of the ,sun is transmitted      
through the vast ,bodies of the ,planets
 without any diminution1 so as to act   
upon all their parts to their very      
centers with the same ,force and        
according to the same ,laws1 as if the  
part upon which it acts were not        
surrounded with the ,body of the        
,planet1 ,the ,rays of ,light1 whether  
they be very small ,bodies projected1 or
 only ,motion or ,force propagated1 are 
moved in right ,lines2 and whenever a   
,ray of ,light is by any ,obstacle      
turned out of its rectilinear way1 it   
will never return into the same         
rectilinear way1 unless perhaps by very 
great accident4 ,and yet ,light is      
transmitted through pellucid solid      
,bodies in right ,lines to very great   
distances4 ,how ,bodies can have a      
sufficient quantity of ,pores for       

producing these ,effects is very        
difficult to conceive1 but perhaps not  
altogether impossible4 ,for the ,colours
 of ,bodies arise from the ,magnitudes  
of the ,particles which reflect them1 as
 was explained above4 ,now if we        
conceive these ,particles of ,bodies to 
be so disposed amongst themselves1 that 
the ,intervals or empty ,spaces between 
them may be equal in magnitude to them  
all2 and that these ,particles may be   
composed of other ,particles much       
smaller1 which have as much empty ,space
 between them as equals all the         
,magnitudes of these smaller ,particles3
 ,and that in like manner these smaller 
,particles are again composed of others 
much smaller1 all which together are    
equal to all the ,pores or empty ,spaces
 between them2 and so on perpetually    
till you come to solid ,particles1 such 
as have no ,pores or empty ,spaces      
within them3 ,and if in any gross ,body 
there be1 for instance1 three such      
degrees of ,particles1 the least of     

which are solid2 this ,body will have   
seven times more ,pores than solid      
,parts4 ,but if there be four such      
degrees of ,particles1 the least of     
which are solid1 the ,body will have    
fifteen times more ,pores than solid    
,parts4 ,if there be five degrees1 the  
,body will have one and thirty times    
more ,pores than solid ,parts4 ,if six  
degrees1 the ,body will have sixty and  
three times more ,pores than solid      
,parts4 ,and so on perpetually4 ,and    
there are other ways of conceiving how  
,bodies may be exceeding porous4 ,but   
what is really their inward ,frame is   
not yet known to us4   ,,prop4 ,,ix4    
,bodies reflect and refract ,light by   
one and the same power1 variously       
exercised in various ,circumstances4    
,this appears by several                
,considerations4 ,first1 ,because when  
,light goes out of ,glass into ,air1 as 
obliquely as it can possibly do4 ,if its
 ,incidence be made still more oblique1 
it becomes totally reflected4 ,for the  

power of the ,glass after it has        
refracted the ,light as obliquely as is 
possible1 if the ,incidence be still    
made more oblique1 becomes too strong to
 let any of its ,rays go through1 and by
 consequence causes total ,reflexions4  
,secondly1 ,because ,light is           
alternately reflected and transmitted by
 thin ,plates of ,glass for many        
,successions1 accordingly as the        
thickness of the ,plate increases in an 
arithmetical ,progression4 ,for here the
 thickness of the ,glass determines     
whether that ,power by which ,glass acts
 upon ,light shall cause it to be       
reflected1 or suffer it to be           
transmitted4 ,and1 ,thirdly1 because    
those ,surfaces of transparent ,bodies  
which have the greatest refracting      
power1 reflect the greatest quantity of 
,light1 as was shewn in the first       
,proposition4   ,,prop4 ,x4  ,if ,light 
be swifter in ,bodies than in ,vacuo1 in
 the proportion of the ,sines which     
measure the ,refraction of the ,bodies1 

the ,forces of the ,bodies to reflect   
and refract ,light1 are very nearly     
proportional to the densities of the    
same ,bodies2 excepting that unctuous   
and sulphureous ,bodies refract more    
than others of this same density4       
,illustration3 ,,fig4 #h4  ,let ,,ab    
represent the refracting plane ,surface 
of any ,body1 and ,,ic a ,ray incident  
very obliquely upon the ,body in ,c1 so 
that the ,angle ,,aci may be infinitely 
little1 and let ,,cr be the refracted   
,ray4 ,from a given ,point ,b           
perpendicular to the refracting ,surface
 erect ,,br meeting with the refracting 
,ray ,,cr in ,r1 and if ,,cr represent  
the ,motion of the refracted ,ray1 and  
this ,motion be distinguish'd into two  
,motions ,,cb and ,,br1 whereof ,,cb is 
parallel to the refracting ,plane1 and  
,,br perpendicular to it3 ,,cb shall    
represent the ,motion of the incident   
,ray1 and ,,br the ,motion generated by 
the ,refraction1 as ,opticians have of  
late explain'd4  ,now if any ,body or   

,thing1 in moving through any ,space of 
a given breadth terminated on both sides
 by two parallel ,planes1 be urged      
forward in all parts of that ,space by  
,forces tending directly forwards       
towards the last ,plane1 and before its 
,incidence on the first ,plane1 had no  
,motion towards it1 or but an infinitely
 little one2 and if the ,forces in all  
parts of that ,space1 between the       
,planes1 be at equal distances from the 
,planes equal to one another1 but at    
several distances be bigger or less in  
any given ,proportion1 the ,motion      
generated by the ,forces in the whole   
passage of the ,body or thing through   
that ,space shall be in a subduplicate  
,proportion of the ,forces1 as          
,mathematicians will easily understand4 
,and therefore1 if the ,space of        
activity of the refracting ,superficies 
of the ,body be consider'd as such a    
,space1 the ,motion of the ,ray         
generated by the refracting ,force of   
the ,body1 during its passage through   

that ,space1 that is1 the ,motion ,,br1 
must be in subduplicate ,proportion of  
that refracting ,force4 ,i say          
therefore1 that the ,square of the ,line
 ,,br1 and by consequence the refracting
 ,force of the ,body1 is very nearly as 
the density of the same ,body4 ,for this
 will appear by the following ,table1   
wherein the ,proportion of the ,sines   
which measure the ,refractions of       
several ,bodies1 the ,square of ,,br1   
supposing ,,cb an unite1 the ,densities 
of the ,bodies estimated by their       
,specifick ,gravities1 and their        
,refractive ,power in respect of their  
,densities are set down in several      
,columns4                               
----------------------------------------
----------------------------------      
,the ,square      ,the       ,the       
of ,,br1 to       density   refractive  
,the ,proportion  which the       and   
,power of                       of the  
,sines of refracting      specifick the 
,body                       ,incidence  

and   force of the    gravity   in      
respect    ,the refracting              
,refraction of   ,body is         of the
    of its       ,bodies4         yellow
 ,light4   proportionate4  ,body4       
density4                                
----------------------------------------
---------------------------------- ,a   
,pseudo-,topazius1                      
being a natural1                        
pellucid1 brittle1    #bc to   #ad      
#a'fii         #d'bg       #cigi   hairy
 ,stone1 of a                           
yellow ,colour4                         
,air4                  #cbja to #cbjj   
#j'jjjfbe      #j'jjab     #ebjh ,glass 
of ,antimony4      #ag to    #i         
#b'efh         #e'bh       #dhfd ,a     
,selenitis4            #fa to   #da     
#a'bac         #b'beb      #echf ,glass 
vulgar4           #ca to   #bj          
#a'djbe        #b'eh       #edcf        
,crystal of the ,rock4    #be to   #af  
#a'dde         #b'fe       #edej ,island
 ,crystal4          #e to    #c         

#a'ggh         #b'gb       #fecf ,sal   
,gemmae4              #ag to   #aa      
#a'chh         #b'adc      #fdgg ,alume4
                  #ce to   #bd          
#a'abfg        #a'gad      #fegj ,borax4
                  #bb to   #ae          
#a'aeaa        #a'gad      #fgaf ,niter4
                  #cb to   #ba          
#a'cde         #a'i        #gjgi        
,dantzick ,vitriol4      #cjc to  #bjj  
#a'bie         #a'gae      #geea ,oil of
 ,vitriol4         #aj to    #g         
#a'jda         #a'g        #fabd ,rain  
,water4            #ebi to  #cif        
#j'ghde        #a'         #ghde ,gum   
,arabick4            #ca to   #ba       
#a'agi         #a'cge      #hegd ,spirit
 of ,wine well                          
rectified4           #ajj to   #gc      
#j'hgfe        #j'hff     #ajaba        
,camphire4                #c to    #b   
#a'be          #j'iif     #abeea ,oil   
,olive4              #bb to   #ae       
#a'aeaa        #j'iac     #abfjg        
,linseed ,oil4            #dj to   #bg  

#a'aidh        #j'icb     #abhai ,spirit
 of ,turpentine4   #be to   #ag         
#a'afbf        #j'hgd     #acbbb ,amber4
                  #ad to    #i          
#a'db          #a'jd      #acfed ,a     
,diamond4             #ajj to   #da     
#d'idi         #c'd       #adeef        
----------------------------------------
----------------------------------  ,the
 ,refraction of the ,air in this ,table 
is determin'd by that of the ,atmosphere
 observed by ,astronomers4 ,for1 if     
,light pass through many refracting     
,substances or ,mediums gradually denser
 and denser1 and terminated with        
parallel ,surfaces1 the ,sum of all the 
,refractions will be equal to the single
 ,refraction which it would have        
suffer'd in passing immediately out of  
the first ,medium into the last4 ,and   
this holds true1 though the ,number of  
the refracting ,substances be increased 
to ,infinity1 and the ,distances from   
one another as much decreased1 so that  
the ,light may be refracted in every    

,point of its ,passage1 and by continual
 ,refractions bent into a ,curve-,line4 
,and therefore the whole ,refraction of 
,light in passing through the           
,atmosphere from the highest and rarest 
,part thereof down to the lowest and    
densest ,part1 must be equal to the     
,refraction which it would suffer in    
passing at like ,obliquity out of a     
,vacuum immediately into ,air of equal  
,density with that in the lowest ,part  
of the ,atmosphere4  ,now1 although a   
,pseudo-,topaz1 a ,selenitis1 ,rock     
,crystal1 ,island ,crystal1 ,vulgar     
,glass 7that is1 ,sand melted together7 
and ,glass of ,antimony1 which are      
terrestrial stony alcalizate ,concretes1
 and ,air which probably arises from    
such ,substances by ,fermentation1 be   
,substances very differing from one     
another in ,density1 yet by this ,table1
 they have their refractive ,powers     
almost in the same ,proportion to one   
another as their ,densities are1        
excepting that the ,refraction of that  

strange ,substance1 ,island ,crystal is 
a little bigger than the rest4 ,and     
particularly ,air1 which is #cejj ,times
 rarer than the ,pseudo-,topaz1 and     
#ddjj ,times rarer than ,glass of       
,antimony1 and #bjjj ,times rarer than  
the ,selenitis1 ,glass vulgar1 or       
,crystal of the ,rock1 has              
notwithstanding its rarity the same     
refractive ,power in respect of its     
,density which those very dense         
,substances have in respect of theirs1  
excepting so far as those differ from   
one another4  ,again1 the ,refraction of
 ,camphire1 ,oil ,olive1 ,linseed ,oil1 
,spirit of ,turpentine and ,amber1 which
 are fat sulphureous unctuous ,bodies1  
and a ,diamond1 which probably is an    
unctuous ,substance coagulated1 have    
their refractive ,powers in ,proportion 
to one another as their ,densities      
without any considerable ,variation4    
,but the refractive ,powers of these    
unctuous ,substances are two or three   
,times greater in respect of their      

,densities than the refractive ,powers  
of the former ,substances in respect of 
theirs4  ,water has a refractive ,power 
in a middle degree between those two    
sorts of ,substances1 and probably is of
 a middle nature4 ,for out of it grow   
all vegetable and animal ,substances1   
which consist as well of sulphureous fat
 and inflamable ,parts1 as of earthy    
lean and alcalizate ones4  ,salts and   
,vitriols have refractive ,powers in a  
middle degree between those of earthy   
,substances and ,water1 and accordingly 
are composed of those two sorts of      
,substances4 ,for by distillation and   
rectification of their ,spirits a great 
,part of them goes into ,water1 and a   
great ,part remains behind in the form  
of a dry fix'd ,earth capable of        
,vitrification4  ,spirit of ,wine has a 
refractive ,power in a middle degree    
between those of ,water and oily        
,substances1 and accordingly seems to be
 composed of both1 united by            
,fermentation2 the ,water1 by means of  

some saline ,spirits with which 'tis    
impregnated1 dissolving the ,oil1 and   
volatizing it by the ,action4 ,for      
,spirit of ,wine is inflamable by means 
of its oily ,parts1 and being distilled 
often from ,salt of ,tartar1 grow by    
every distillation more and more aqueous
 and phlegmatick4 ,and ,chymists        
observe1 that ,vegetables 7as ,lavender1
 ,rue1 ,marjoram1 c47 distilled per se1 
before fermentation yield ,oils without 
any burning ,spirits1 but after         
fermentation yield ardent ,spirits      
without ,oils3 ,which shews1 that their 
,oil is by fermentation converted into  
,spirit4 ,they find also1 that if ,oils 
be poured in a small quantity upon      
fermentating ,vegetables1 they distil   
over after fermentation in the form of  
,spirits4  ,so then1 by the foregoing   
,table1 all ,bodies seem to have their  
refractive ,powers proportional to their
 ,densities1 7or very nearly27 excepting
 so far as they partake more or less of 
sulphureous oily ,particles1 and thereby

 have their refractive ,power made      
greater or less4 ,whence it seems       
rational to attribute the refractive    
,power of all ,bodies chiefly1 if not   
wholly1 to the sulphureous ,parts with  
which they abound4 ,for it's probable   
that all ,bodies abound more or less    
with ,sulphurs4 ,and as ,light          
congregated by a ,burning-glass acts    
most upon sulphureous ,bodies1 to turn  
them into ,fire and ,flame2 so1 since   
all ,action is mutual1 ,sulphurs ought  
to act most upon ,light4 ,for that the  
action between ,light and ,bodies is    
mutual1 may appear from this            
,consideration2 ,that the densest       
,bodies which refract and reflect ,light
 most strongly1 grow hottest in the     
,summer ,sun1 by the action of the      
refracted or reflected ,light4  ,i have 
hitherto explain'd the power of ,bodies 
to reflect and refract1 and shew'd1 that
 thin transparent ,plates1 ,fibres1 and 
,particles1 do1 according to their      
several thicknesses and densities1      

reflect several sorts of ,rays1 and     
thereby appear of several ,colours2 and 
by consequence that nothing more is     
requisite for producing all the ,colours
 of natural ,bodies1 than the several   
sizes and densities of their transparent
 ,particles4 ,but whence it is that     
these ,plates1 ,fibres1 and ,particles1 
do1 according to their several          
thicknesses and densities1 reflect      
several sorts of ,rays1 ,i have not yet 
explain'd4 ,to give some insight into   
this matter1 and make way for           
understanding the next part of this     
,book1 ,i shall conclude this part with 
a few more ,propositions4 ,those which  
preceded respect the nature of ,bodies1 
these the nature of ,light3 ,for both   
must be understood1 before the reason of
 their ,actions upon one another can be 
known4 ,and because the last            
,proposition depended upon the velocity 
of ,light1 ,i will begin with a         
,proposition of that kind4   ,,prop4    
,,xi4  ,light is propagated from        

luminous ,bodies in time1 and spends    
about seven or eight ,minutes of an     
,hour in passing from the ,sun to the   
,earth4  ,this was observed first by    
,roemer1 and then by others1 by means of
 the ,eclipses of the ,satellites of    
,jupiter4 ,for these ,eclipses1 when the
 ,earth is between the ,sun and         
,jupiter1 happen about seven or eight   
,minutes sooner than they ought to do by
 the ,tables1 and when the ,earth is    
beyond the ,sun they happen about seven 
or eight ,minutes later than they ought 
to do2 the reason being1 that the ,light
 of the ,satellites has farther to go in
 the latter case than in the former by  
the ,diameter of the ,earth's ,orbit4   
,some inequalities of time may arise    
from the ,excentricities of the ,orbs of
 the ,satellites2 but those cannot      
answer in all the ,satellites1 and at   
all times to the ,position and ,distance
 of the ,earth from the ,sun4 ,the mean 
motions of ,jupiter's ,satellites is    
also swifter in his descent from his    

,aphelium to his ,perihelium1 than in   
his ascent in the other half of his     
,orb4 ,but this inequality has no       
respect to the position of the ,earth1  
and in the three interior ,satellites is
 insensible1 as ,i find by computation  
from the ,theory of their ,gravity4     
,,prop4 ,,xii4  ,every ,ray of ,light in
 its passage through any refracting     
,surface is put into a certain transient
 ,constitution or ,state1 which in the  
progress of the ,ray returns at equal   
,intervals1 and disposes the ,ray at    
every return to be easily transmitted   
through the next refracting ,surface1   
and between the returns to be easily    
reflected by it4  ,this is manifest by  
the #eth1 #ith1 #abth1 and #aeth        
,observations4 ,for by those            
,observations it appears1 that one and  
the same sort of ,rays at equal ,angles 
of ,incidence on any thin transparent   
,plate1 is alternately reflected and    
transmitted for many ,successions       
accordingly as the thickness of the     

,plate increases in arithmetical        
,progression of the ,numbers1 #j1 #a1   
#b1 #c1 #d1 #e1 #f1 #g1 #h1 c4 so that  
if the first ,reflexion 7that which     
makes the first or innermost of the     
,rings of ,colours there described7 be  
made at the thickness #a1 the ,rays     
shall be transmitted at the thicknesses 
#j1 #b1 #d1 #f1 #h1 #aj1 #ab1 c4 and    
thereby make the central ,spot and      
,rings of ,light1 which appear by       
transmission1 and be reflected at the   
thickness #a1 #c1 #e1 #g1 #i1 #aa1 c4   
and thereby make the ,rings which appear
 by ,reflexion4 ,and this alternate     
,reflexion and ,transmission1 as ,i     
gather by the #bdth ,observation1       
continues for above an hundred          
vicissitudes1 and by the ,observations  
in the next part of this ,book1 for many
 thousands1 being propagated from one   
,surface of a ,glass ,plate to the      
other1 though the thickness of the      
,plate be a quarter of an ,inch or      
above3 ,so that this alternation seems  

to be propagated from every refracting  
,surface to all distances without end or
 limitation4  ,this alternate ,reflexion
 and ,refraction depends on both the    
,surfaces of every thin ,plate1 because 
it depends on their distance4 ,by the   
#bast ,observation1 if either ,surface  
of a thin ,plate of ,muscovy ,glass be  
wetted1 the ,colours caused by the      
alternate ,reflexion and ,refraction    
grow faint1 and therefore it depends on 
them both4  ,it is therefore perform'd  
at the second ,surface2 for if it were  
perform'd at the first1 before the ,rays
 arrive at the second1 it would not     
depend on the second4  ,it is also      
influenced by some action or            
disposition1 propagated from the first  
to the second1 because otherwise at the 
second it would not depend on the first4
 ,and this action or disposition1 in its
 propagation1 intermits and returns by  
equal ,intervals1 because in all its    
progress it inclines the ,ray at one    
distance from the first ,surface to be  

reflected by the second1 at another to  
be transmitted by it1 and that by equal 
,intervals for innumerable vicissitudes4
 ,and because the ,ray is disposed to   
,reflexion at the distances #a1 #c1 #e1 
#g1 #i1 c4 and to ,transmission at the  
distances #j1 #b1 #d1 #f1 #h1 #aj1 c4   
7for its transmission through the first 
,surface1 is at the distance #j1 and it 
is transmitted through both together1 if
 their distance be infinitely little or 
much less than #a7 the disposition to be
 transmitted at the distances #b1 #d1   
#f1 #h1 #aj1 c4 is to be accounted a    
return of the same disposition which the
 ,ray first had at the distance #j1 that
 is at its transmission through the     
first refracting ,surface4 ,all which is
 the thing ,i would prove4  ,what kind  
of action or disposition this is2       
,whether it consists in a circulating or
 a vibrating motion of the ,ray1 or of  
the ,medium1 or something else1 ,i do   
not here enquire4 ,those that are averse
 from assenting to any new ,discoveries1

 but such as they can explain by an     
,hypothesis1 may for the present        
suppose1 that as ,stones by falling upon
 ,water put the ,water into an          
undulating ,motion1 and all ,bodies by  
percussion excite vibrations in the     
,air2 so the ,rays of ,light1 by        
impinging on any refracting or          
reflecting ,surface1 excite vibrations  
in the refracting or reflecting ,medium 
or ,substance1 and by exciting them     
agitate the solid parts of the          
refracting or reflecting ,body1 and by  
agitating them cause the ,body to grow  
warm or hot2 that the vibrations thus   
excited are propagated in the refracting
 or reflecting ,medium or ,substance1   
much after the manner that vibrations   
are propagated in the ,air for causing  
,sound1 and move faster than the ,rays  
so as to overtake them2 and that when   
any ,ray is in that part of the         
vibration which conspires with its      
,motion1 it easily breaks through a     
refracting ,surface1 but when it is in  

the contrary part of the vibration which
 impedes its ,motion1 it is easily      
reflected2 and1 by consequence1 that    
every ,ray is successively disposed to  
be easily reflected1 or easily          
transmitted1 by every vibration which   
overtakes it4 ,but whether this         
,hypothesis be true or false ,i do not  
here consider4 ,i content my self with  
the bare ,discovery1 that the ,rays of  
,light are by some cause or other       
alternately disposed to be reflected or 
refracted for many vicissitudes4        
,,definition4  ,the returns of the      
disposition of any ,ray to be reflected 
,i will call its ,fits of easy          
,reflexion1 and those of its disposition
 to be transmitted its ,fits of easy    
,transmission1 and the space it passes  
between every return and the next       
return1 the ,interval of its ,fits4     
,,prop4 ,,xiii4  ,the reason why the    
,surfaces of all thick transparent      
,bodies reflect part of the ,light      
incident on them1 and refract the rest1 

is1 that some ,rays at their ,incidence 
are in ,fits of easy ,reflexion1 and    
others in ,fits of easy ,transmission4  
,this may be gather'd from the #bdth    
,observation1 where the ,light reflected
 by thin ,plates of ,air and ,glass1    
which to the naked ,eye appear'd evenly 
white all over the ,plate1 did through a
 ,prism appear waved with many          
,successions of ,light and ,darkness    
made by alternate ,fits of easy         
,reflexion and easy ,transmission1 the  
,prism severing and distinguishing the  
,waves of which the white reflected     
,light was composed1 as was explain'd   
above4  ,and hence ,light is in ,fits of
 easy ,reflexion and easy ,transmission1
 before its ,incidence on transparent   
,bodies4 ,and probably it is put into   
such fits at its first emission from    
luminous ,bodies1 and continues in them 
during all its progress4 ,for these     
,fits are of a lasting nature1 as will  
appear by the next part of this ,book4  
,in this ,proposition ,i suppose the    

transparent ,bodies to be thick2 because
 if the thickness of the ,body be much  
less than the ,interval of the ,fits of 
easy ,reflexion and ,transmission of the
 ,rays1 the ,body loseth its reflecting 
power4 ,for if the ,rays1 which at their
 entering into the ,body are put into   
,fits of easy ,transmission1 arrive at  
the farthest ,surface of the ,body      
before they be out of those ,fits1 they 
must be transmitted4 ,and this is the   
reason why ,bubbles of ,water lose their
 reflecting power when they grow very   
thin2 and why all opake ,bodies1 when   
reduced into very small parts1 become   
transparent4   ,,prop4 ,,xiv4  ,those   
,surfaces of transparent ,bodies1 which 
if the ,ray be in a ,fit of ,refraction 
do refract it most strongly1 if the ,ray
 be in a ,fit of ,reflexion do reflect  
it most easily4  ,for we shewed above1  
in ,prop4 #h4 that the cause of         
,reflexion is not the impinging of      
,light on the solid impervious parts of 
,bodies1 but some other power by which  

those solid parts act on ,light at a    
distance4 ,we shewed also in ,prop4 #i4 
that ,bodies reflect and refract ,light 
by one and the same power1 variously    
exercised in various circumstances2 and 
in ,prop4 #a4 that the most strongly    
refracting ,surfaces reflect the most   
,light3 ,all which compared together    
evince and rarify both this and the last
 ,proposition4   ,,prop4 ,,xv4  ,in any 
one and the same sort of ,rays1 emerging
 in any ,angle out of any refracting    
,surface into one and the same ,medium1 
the ,interval of the following ,fits of 
easy ,reflexion and ,transmission are   
either accurately or very nearly1 as the
 ,rectangle of the ,secant of the ,angle
 of ,refraction1 and of the ,secant of  
another ,angle1 whose ,sine is the first
 of #ajf arithmetical mean              
,proportionals1 between the ,sines of   
,incidence and ,refraction1 counted from
 the ,sine of ,refraction4  ,this is    
manifest by the #gth and #aith          
,observations4   ,,prop4 ,,xvi4  ,in    

several sorts of ,rays emerging in equal
 ,angles out of any refracting ,surface 
into the same ,medium1 the ,intervals of
 the following ,fits of easy ,reflexion 
and easy ,transmission are either       
accurately1 or very nearly1 as the      
,cube-,roots of the ,squares of the     
lengths of a ,chord1 which found the    
,notes in an ,eight1 sol1 la1 fa1 sol1  
la1 mi1 fa1 sol1 with all their         
intermediate degrees answering to the   
,colours of those ,rays1 according to   
the ,analogy described in the seventh   
,experiment of the second ,part of the  
first ,book4  ,this is manifest by the  
#acth and #adth ,observations4   ,,prop4
 ,,xvii4  ,if ,rays of any sort pass    
perpendicularly into several ,mediums1  
the ,intervals of the ,fits of easy     
,reflexion and ,transmission in any one 
,medium1 are to those ,intervals in any 
other1 as the ,sine of ,incidence to the
 ,sine of ,refraction1 when the ,rays   
pass out of the first of those two      
,mediums into the second4  ,this is     

manifest by the #ajth ,observation4     
,,prop4 ,,xviii4  ,if the ,rays which   
paint the ,colour in the ,confine of    
yellow and orange pass perpendicularly  
out of any ,medium into ,air1 the       
,intervals of their ,fits of easy       
,reflexion are the #a_/hijjjth part of  
an ,inch4 ,and of the same length are   
the ,intervals of their ,fits of easy   
,transmission4  ,this is manifest by the
 #fth ,observation4 ,from these         
,propositions it is easy to collect the 
,intervals of the ,fits of easy         
,reflexion and easy ,transmission of any
 sort of ,rays refracted in any angle   
into any ,medium2 and thence to know1   
whether the ,rays shall be reflected or 
transmitted at their subsequent         
,incidence upon any other pellucid      
,medium4 ,which thing1 being useful for 
understanding the next part of this     
,book1 was here to be set down4 ,and for
 the same reason ,i add the two         
following ,propositions4   ,,prop4      
,,xix4  ,if any sort of ,rays falling on

 the polite ,surface of any pellucid    
,medium be reflected back1 the ,fits of 
easy ,reflexion1 which they have at the 
point of ,reflexion1 shall still        
continue to return2 and the ,returns    
shall be at distances from the point of 
,reflexion in the arithmetical          
progression of the ,numbers #b1 #d1 #f1 
#h1 #aj1 #ab1 c4 and between these ,fits
 the ,rays shall be in ,fits of easy    
,transmission4  ,for since the ,fits of 
easy ,reflexion and easy ,transmission  
are of a returning nature1 there is no  
reason why these ,fits1 which continued 
till the ,ray arrived at the reflecting 
,medium1 and there inclined the ,ray to 
,reflexion1 should there cease4 ,and if 
the ,ray at the point of ,reflexion was 
in a ,fit of easy ,reflexion1 the       
progression of the distances of these   
,fits from that point must begin from   
#j1 and so be of the ,numbers #j1 #b1   
#d1 #f1 #h1 c4 ,and therefore the       
progression of the distances of the     
intermediate ,fits of easy              

,transmission1 reckon'd from the same   
point1 must be in the progression of the
 odd ,numbers #a1 #c1 #e1 #g1 #i1 c4    
contrary to what happens when the ,fits 
are propagated from points of           
,refraction4   ,,prop4 ,,xx4  ,the      
,intervals of the ,fits of easy         
,reflexion and easy ,transmission1      
propagated from points of ,reflexion    
into any ,medium1 are equal to the      
,intervals of the like ,fits1 which the 
same ,rays would have1 if refracted into
 the same ,medium in ,angles of         
,refraction equal to their ,angles of   
,reflexion4  ,for when ,light is        
reflected by the second ,surface of thin
 ,plates1 it goes out afterwards freely 
at the first ,surface to make the ,rings
 of ,colours which appear by ,reflexion2
 and1 by the freedom of its egress1     
makes the ,colours of these ,rings more 
vivid and strong than those which appear
 on the other side of the ,plates by the
 transmitted ,light4 ,the reflected     
,rays are therefore in ,fits of easy    

,transmission at their egress2 which    
would not always happen1 if the         
,intervals of the ,fits within the      
,plate after ,reflexion were not equal1 
both in length and number1 to their     
,intervals before it4 ,and this confirms
 also the proportions set down in the   
former ,proposition4 ,for if the ,rays  
both in going in and out at the first   
,surface be in ,fits of easy            
,transmission1 and the ,intervals and   
,numbers of those ,fits between the     
first and second ,surface1 before and   
after ,reflexion1 be equal1 the         
distances of the ,fits of easy          
,transmission from either ,surface1 must
 be in the same progression after       
,reflexion as before2 that is1 from the 
first ,surface which transmitted them in
 the progression of the even ,numbers   
#j1 #b1 #d1 #f1 #h1 c4 and from the     
second which reflected them1 in that of 
the odd ,numbers #a1 #c1 #e1 #g1 c4 ,but
 these two ,propositions will become    
much more evident by the ,observations  

in the following part of this ,book4    
,,the  ,,second ,,book  ,,of  ,,opticks 
,,part ,,iv4  ,observations concerning  
the ,reflexions and ,colours of thick   
transparent polish'd ,plates4  ,there is
 no ,glass or ,speculum how well soever 
polished1 but1 besides the ,light which 
it refracts or reflects regularly1      
scatters every way irregularly a faint  
,light1 by means of which the polish'd  
,surface1 when illuminated in a dark    
room by a beam of the ,sun's ,light1 may
 be easily seen in all positions of the 
,eye4 ,there are certain ,phaenomena of 
this scatter'd ,light1 which when ,i    
first observed them1 seem'd very strange
 and surprizing to me4 ,my ,observations
 were as follows4  ,obs4 #a4 ,the ,sun  
shining into my darken'd ,chamber       
through a hole one third of an ,inch    
wide1 ,i let the intromitted beam of    
,light fall perpendicularly upon a      
,glass ,speculum ground concave on one  
side and convex on the other1 to a      
,sphere of five ,feet and eleven ,inches

 ,radius1 and ,quick-silver'd over on   
the convex side4 ,and holding a white   
opake ,chart1 or a ,quire of ,paper at  
the center of the ,spheres to which the 
,speculum was ground1 that is1 at the   
distance of about five ,feet and eleven 
,inches from the ,speculum1 in such     
manner1 that the beam of ,light might   
pass through a little hole made in the  
middle of the ,chart to the ,speculum1  
and thence be reflected back to the same
 hole3 ,i observed upon the ,chart four 
or five concentric ,irises or ,rings of 
,colours1 like ,rain-bows1 encompassing 
the hole much after the manner that     
those1 which in the fourth and following
 ,observations of the first part of this
 ,book appear'd between the             
,object-glasses1 encompassed the black  
,spot1 but yet larger and fainter than  
those4 ,these ,rings as they grew larger
 and larger became diluter and fainter1 
so that the fifth was scarce visible4   
,yet sometimes1 when the ,sun shone very
 clear1 there appear'd faint ,lineaments

 of a sixth and seventh4 ,if the        
distance of the ,chart from the         
,speculum was much greater or much less 
than that of six ,feet1 the ,rings      
became dilute and vanish'd4 ,and if the 
distance of the ,speculum from the      
,window was much greater than that of   
six ,feet1 the reflected beam of ,light 
would be so broad at the distance of six
 ,feet from the ,speculum where the     
,rings appear'd1 as to obscure one or   
two of the innermost ,rings4 ,and       
therefore ,i usually placed the         
,speculum at about six ,feet from the   
,window2 so that its ,focus might there 
fall in with the center of its concavity
 at the ,rings upon the ,chart4 ,and    
this ,posture is always to be understood
 in the following ,observations where no
 other is express'd4  ,obs4 #b4 ,the    
,colours of these ,rain-bows succeeded  
one another from the center outwards1 in
 the same form and order with those     
which were made in the ninth            
,observation of the first ,part of this 

,book by ,light not reflected1 but      
transmitted through the two             
,object-glasses4 ,for1 first1 there was 
in their common center a white round    
,spot of faint ,light1 something broader
 than the reflected beam of ,light1     
which beam sometimes fell upon the      
middle of the ,spot1 and sometimes by a 
little inclination of the ,speculum     
receded from the middle1 and left the   
,spot white to the center4  ,this white 
,spot was immediately encompassed with a
 dark grey or russet1 and that dark grey
 with the ,colours of the first ,iris2  
which ,colours on the inside next the   
dark grey were a little violet and      
indigo1 and next to that a blue1 which  
on the outside grew pale1 and then      
succeeded a little greenish yellow1 and 
after that a brighter yellow1 and then  
on the outward edge of the ,iris a red  
which on the outside inclined to purple4
  ,this ,iris was immediately           
encompassed with a second1 whose        
,colours were in order from the inside  

outwards1 purple1 blue1 green1 yellow1  
light red1 a red mix'd with purple4     
,then immediately follow'd the ,colours 
of the third ,iris1 which were in order 
outwards a green inclining to purple1 a 
good green1 and a red more bright than  
that of the former ,iris4  ,the fourth  
and fifth ,iris seem'd of a bluish green
 within1 and red without1 but so faintly
 that it was difficult to discern the   
,colours4  ,obs4 #c4 ,measuring the     
,diameters of these ,rings upon the     
,chart as accurately as ,i could1 ,i    
found them also in the same proportion  
to one another with the ,rings made by  
,light transmitted through the two      
,object-glasses4 ,for the ,diameters of 
the four first of the bright ,rings     
measured between the brightest parts of 
their ,orbits1 at the distance of six   
,feet from the ,speculum were #a-aa_/af1
 #b-c_/h1 #b-aa_/ab1 #c-c_/h ,inches1   
whose ,squares are in arithmetical      
progression of the numbers #a1 #b1 #c1  
#d4 ,if the white circular ,spot in the 

middle be reckon'd amongst the ,rings1  
and its central ,light1 where it seems  
to be most luminous1 be put equipollent 
to an infinitely little ,ring2 the      
,squares of the ,diameters of the ,rings
 will be in the progression #j1 #a1 #b1 
#c1 #d1 c4 ,i measured also the         
,diameters of the dark ,circles between 
these luminous ones1 and found their    
,squares in the progression of the      
numbers #a_/b1 #a-a_/b1 #b-a_/b1        
#c-a_/b1 c4 the ,diameters of the first 
four at the distance of six ,feet from  
the ,speculum1 being #a-c_/af1 #b-a_/af1
 #b-b_/c1 #c-c_/bj ,inches4 ,if the     
distance of the ,chart from the         
,speculum was increased or diminished1  
the ,diameters of the ,circles were     
increased or diminished proportionally4 
,obs4 #d4 ,by the analogy between these 
,rings and those described in the       
,observations of the first ,part of this
 ,book1 ,i suspected that there were    
many more of them which spread into one 
another1 and by interfering mix'd their 

,colours1 and diluted one another so    
that they could not be seen apart4 ,i   
viewed them therefore through a ,prism1 
as ,i did those in the #bdth            
,observation of the first ,part of this 
,book4 ,and when the ,prism was so      
placed as by refracting the ,light of   
their mix'd ,colours to separate them1  
and distinguish the ,rings from one     
another1 as it did those in that        
,observation1 ,i could then see them    
distincter than before1 and easily      
number eight or nine of them1 and       
sometimes twelve or thirteen4 ,and had  
not their ,light been so very faint1 ,i 
question not but that ,i might have seen
 many more4  ,obs4 #e4 ,placing a ,prism
 at the ,window to refract the          
intromitted beam of ,light1 and cast the
 oblong ,spectrum of ,colours on the    
,speculum3 ,i covered the ,speculum with
 a black ,paper which had in the middle 
of it a hole to let any one of the      
,colours pass through to the ,speculum1 
whilst the rest were intercepted by the 

,paper4 ,and now ,i found ,rings of that
 ,colour only which fell upon the       
,speculum4 ,if the ,speculum was        
illuminated with red1 the ,rings were   
totally red with dark ,intervals1 if    
with blue they were totally blue1 and so
 of the other ,colours4 ,and when they  
were illuminated with any one ,colour1  
the ,squares of their ,diameters        
measured between their most luminous    
,parts1 were in the arithmetical        
,progression of the ,numbers1 #j1 #a1   
#b1 #c1 #d and the ,squares of the      
,diameters of their dark ,intervals in  
the ,progression of the intermediate    
,numbers #a_/b1 #a-a_/b1 #b-a_/b1       
#c-a_/b4 ,but if the ,colour was varied1
 they varied their ,magnitude4 ,in the  
red they were largest1 in the indigo and
 violet least1 and in the intermediate  
,colours yellow1 green1 and blue1 they  
were of several intermediate ,bignesses 
answering to the ,colour1 that is1      
greater in yellow than in green1 and    
greater in green than in blue4 ,and     

hence ,i knew1 that when the ,speculum  
was illuminated with white ,light1 the  
red and yellow on the outside of the    
,rings were produced by the least       
refrangible ,rays1 and the blue and     
violet by the most refrangible1 and that
 the ,colours of each ,ring spread into 
the ,colours of the neighbouring ,rings 
on either side1 after the manner        
explain'd in the first and second ,part 
of this ,book1 and by mixing diluted one
 another so that they could not be      
distinguish'd1 unless near the ,center  
where they were least mix'd4 ,for in    
this ,observation ,i could see the      
,rings more distinctly1 and to a greater
 ,number than before1 being able in the 
yellow ,light to number eight or nine of
 them1 besides a faint shadow of a      
tenth4 ,to satisfy my self how much the 
,colours of the several ,rings spread   
into one another1 ,i measured the       
,diameters of the second and third      
,rings1 and found them when made by the 
,confine of the red and orange to be to 

the same ,diameters when made by the    
,confine of blue and indigo1 as #i to   
#h1 or thereabouts4 ,for it was hard to 
determine this ,proportion accurately4  
,also the ,circles made successively by 
the red1 yellow1 and green1 differ'd    
more from one another than those made   
successively by the green1 blue1 and    
indigo4 ,for the ,circle made by the    
violet was too dark to be seen4 ,to     
carry on the ,computation1 let us       
therefore suppose that the ,differences 
of the ,diameters of the ,circles made  
by the outmost red1 the ,confine of red 
and orange1 the ,confine of orange and  
yellow1 the ,confine of yellow and      
green1 the ,confine of green and blue1  
the ,confine of blue and indigo1 the    
,confine of indigo and violet1 and      
outmost violet1 are in proportion as the
 ,differences of the ,lengths of a      
,monochord which sound the ,tones in an 
,eight2 sol1 la1 fa1 sol1 la1 mi1 fa1   
sol1 that is1 as the ,numbers #a_/i1    
#a_/ah1 #a_/ab1 #a_/ab1 #b_/bg1 #a_/bg1 

#a_/ah4 ,and if the ,diameter of the    
,circle made by the ,confine of red and 
orange be #i;,a1 and that of the ,circle
 made by the ,confine of blue and indigo
 be #h;,a as above2 their difference    
#i;,a-#h;,a will be to the difference of
 the ,diameters of the ,circles made by 
the outmost red1 and by the ,confine of 
red and orange1 as #a_/ah  #a_/ab       
#a_/ab  #b_/bg to #a_/i1 that is as     
#h_/bg to #a_/i1 or #h to #c1 and to the
 difference of the ,circles made by the 
outmost violet1 and by the ,confine of  
blue and indigo1 as #a_/ah  #a_/ab      
#a_/ab  #b_/bg to #a_/bg  #a_/ah1 that  
is1 as #h_/bg to #e_/ed1 or as #af to   
#e4 ,and therefore these differences    
will be #c_/h;,a and #e_/af;,a4 ,add the
 first to #i;,a and subduct the last    
from #h;,a1 and you will have the       
,diameters of the ,circles made by the  
least and most refrangible ,rays        
#ge_/h;,a and 77#fa-a_/b7_/h7;,a4 ,these
 diameters are therefore to one another 
as #ge to #fa-a_/b or #ej to #da1 and   

their ,squares as #bejj to #afha1 that  
is1 as #c to #b very nearly4 ,which     
proportion differs not much from the    
proportion of the ,diameters of the     
,circles made by the outmost red and    
outmost violet1 in the #acth            
,observation of the first part of this  
,book4  ,obs4 #f4 ,placing my ,eye where
 these ,rings appear'd plainest1 ,i saw 
the ,speculum tinged all over with      
,waves of ,colours1 7red1 yellow1 green1
 blue27 like those which in the         
,observations of the first part of this 
,book appeared between the              
,object-glasses1 and upon ,bubbles of   
,water1 but much larger4 ,and after the 
manner of those1 they were of various   
magnitudes in various ,positions of the 
,eye1 swelling and shrinking as ,i moved
 my ,eye this way and that way4 ,they   
were formed like ,arcs of concentrick   
,circles1 as those were2 and when my    
,eye was over against the center of the 
concavity of the ,speculum1 7that is1 #e
 ,feet and #aj ,inches distant from the 

,speculum17 their common center was in a
 right ,line with that center of        
concavity1 and with the hole in the     
,window4 ,but in other postures of my   
,eye their center had other positions4  
,they appear'd by the ,light of the     
,clouds propagated to the ,speculum     
through the hole in the ,window2 and    
when the ,sun shone through that hole   
upon the ,speculum1 his ,light upon it  
was of the ,colour of the ,ring whereon 
it fell1 but by its splendor obscured   
the ,rings made by the ,light of the    
,clouds1 unless when the ,speculum was  
removed to a great distance from the    
,window1 so that his ,light upon it     
might be broad and faint4 ,by varying   
the position of my ,eye1 and moving it  
nearer to or farther from the direct    
beam of the ,sun's ,light1 the ,colour  
of the ,sun's reflected ,light          
constantly varied upon the ,speculum1 as
 it did upon my ,eye1 the same ,colour  
always appearing to a ,bystander upon my
 ,eye which to me appear'd upon the     

,speculum4 ,and thence ,i knew that the 
,rings of ,colours upon the ,chart were 
made by these reflected ,colours1       
propagated thither from the ,speculum in
 several ,angles1 and that their        
production depended not upon the        
termination of ,light and ,shadow4      
,obs4 #g4 ,by the ,analogy of all these 
,phaenomena with those of the like      
,rings of ,colours described in the     
first part of this ,book1 it seemed to  
me that these ,colours were produced by 
this thick ,plate of ,glass1 much after 
the manner that those were produced by  
very thin ,plates4 ,for1 upon trial1 ,i 
found that if the ,quick-silver were    
rubb'd off from the backside of the     
,speculum1 the ,glass alone would cause 
the same ,rings of ,colours1 but much   
more faint than before2 and therefore   
the ,phaenomenon depends not upon the   
,quick-silver1 unless so far as the     
,quick-silver by increasing the         
,reflexion of the backside of the ,glass
 increases the ,light of the ,rings of  

,colours4 ,i found also that a ,speculum
 of ,metal without ,glass made some     
,years since for optical uses1 and very 
well wrought1 produced none of those    
,rings2 and thence ,i understood that   
these ,rings arise not from one specular
 ,surface alone1 but depend upon the two
 ,surfaces of the ,plate of ,glass      
whereof the ,speculum was made1 and upon
 the thickness of the ,glass between    
them4 ,for as in the #gth and #aith     
,observations of the first part of this 
,book a thin ,plate of ,air1 ,water1 or 
,glass of an even thickness appeared of 
one ,colour when the ,rays were         
perpendicular to it1 of another when    
they were a little oblique1 of another  
when more oblique1 of another when still
 more oblique1 and so on2 so here1 in   
the sixth ,observation1 the ,light which
 emerged out of the ,glass in several   
,obliquities1 made the ,glass appear of 
several ,colours1 and being propagated  
in those ,obliquities to the ,chart1    
there painted ,rings of those ,colours4 

,and as the reason why a thin ,plate    
appeared of several ,colours in several 
,obliquities of the ,rays1 was1 that the
 ,rays of one and the same sort are     
reflected by the thin ,plate at one     
obliquity and transmitted at another1   
and those of other sorts transmitted    
where these are reflected1 and reflected
 where these are transmitted3 ,so the   
reason why the thick ,plate of ,glass   
whereof the ,speculum was made did      
appear of various ,colours in various   
,obliquities1 and in those ,obliquities 
propagated those ,colours to the ,chart1
 was1 that the ,rays of one and the same
 sort did at one ,obliquity emerge out  
of the ,glass1 at another did not       
emerge1 but were reflected back towards 
the ,quick-silver by the hither ,surface
 of the ,glass1 and accordingly as the  
,obliquity became greater and greater1  
emerged and were reflected alternately  
for many ,successions2 and that in one  
and the same ,obliquity the ,rays of one
 sort were reflected1 and those of      

another transmitted4 ,this is manifest  
by the fifth ,observation of this part  
of this ,book4 ,for in that             
,observation1 when the ,speculum was    
illuminated by any one of the prismatick
 ,colours1 that ,light made many ,rings 
of the same ,colour upon the ,chart with
 dark ,intervals1 and therefore at its  
emergence out of the ,speculum was      
alternately transmitted and not         
transmitted from the ,speculum to the   
,chart for many ,successions1 according 
to the various ,obliquities of its      
,emergence4 ,and when the ,colour cast  
on the ,speculum by the ,prism was      
varied1 the ,rings became of the ,colour
 cast on it1 and varied their bigness   
with their ,colour1 and therefore the   
,light was now alternately transmitted  
and not transmitted from the ,speculum  
to the ,chart at other ,obliquities than
 before4 ,it seemed to me therefore that
 these ,rings were of one and the same  
original with those of thin ,plates1 but
 yet with this difference1 that those of

 thin ,plates are made by the alternate 
,reflexions and ,transmissions of the   
,rays at the second ,surface of the     
,plate1 after one passage through it2   
but here the ,rays go twice through the 
,plate before they are alternately      
reflected and transmitted4 ,first1 they 
go through it from the first ,surface to
 the ,quick-silver1 and then return     
through it from the ,quick-silver to the
 first ,surface1 and there are either   
transmitted to the ,chart or reflected  
back to the ,quick-silver1 accordingly  
as they are in their ,fits of easy      
,reflexion or ,transmission when they   
arrive at that ,surface4 ,for the       
,intervals of the ,fits of the ,rays    
which fall perpendicularly on the       
,speculum1 and are reflected back in the
 same perpendicular ,lines1 by reason of
 the equality of these ,angles and      
,lines1 are of the same length and      
number within the ,glass after          
,reflexion as before1 by the #aith      
,proposition of the third part of this  

,book4 ,and therefore since all the     
,rays that enter through the first      
,surface are in their ,fits of easy     
,transmission at their entrance1 and as 
many of these as are reflected by the   
second are in their ,fits of easy       
,reflexion there1 all these must be     
again in their ,fits of easy            
,transmission at their return to the    
first1 and by consequence there go out  
of the ,glass to the ,chart1 and form   
upon it the white ,spot of ,light in the
 center of the ,rings4 ,for the reason  
holds good in all sorts of ,rays1 and   
therefore all sorts must go out         
promiscuously to that ,spot1 and by     
their mixture cause it to be white4 ,but
 the ,intervals of the ,fits of those   
,rays which are reflected more obliquely
 than they enter1 must be greater after 
,reflexion than before1 by the #aeth and
 #bjth ,propositions4 ,and thence it may
 happen that the ,rays at their return  
to the first ,surface1 may in certain   
,obliquities be in ,fits of easy        

,reflexion1 and return back to the      
,quick-silver1 and in other intermediate
 ,obliquities be again in ,fits of easy 
,transmission1 and so go out to the     
,chart1 and paint on it the ,rings of   
,colours about the white ,spot4 ,and    
because the ,intervals of the ,fits at  
equal obliquities are greater and fewer 
in the less refrangible ,rays1 and less 
and more numerous in the more           
refrangible1 therefore the less         
refrangible at equal obliquities shall  
make fewer ,rings than the more         
refrangible1 and the ,rings made by     
those shall be larger than the like     
number of ,rings made by these2 that is1
 the red ,rings shall be larger than the
 yellow1 the yellow than the green1 the 
green than the blue1 and the blue than  
the violet1 as they were really found to
 be in the fifth ,observation4 ,and     
therefore the first ,ring of all        
,colours encompassing the white ,spot of
 ,light shall be red without any violet 
within1 and yellow1 and green1 and blue 

in the middle1 as it was found in the   
second ,observation2 and these ,colours 
in the second ,ring1 and those that     
follow1 shall be more expanded1 till    
they spread into one another1 and blend 
one another by interfering4  ,these seem
 to be the reasons of these ,rings in   
general2 and this put me upon observing 
the thickness of the ,glass1 and        
considering whether the dimensions and  
proportions of the ,rings may be truly  
derived from it by computation4  ,obs4  
#h4 ,i measured therefore the thickness 
of this concavo-convex ,plate of ,glass1
 and found it every where #a_/d of an   
,inch precisely4 ,now1 by the sixth     
,observation of the first ,part of this 
,book1 a thin ,plate of ,air transmits  
the brightest ,light of the first ,ring1
 that is1 the bright yellow1 when its   
thickness is the #a_/hijjjth part of an 
,inch2 and by the tenth ,observation of 
the same ,part1 a thin ,plate of ,glass 
transmits the same ,light of the same   
,ring1 when its thickness is less in    

proportion of the ,sine of ,refraction  
to the ,sine of ,incidence1 that is1    
when its thickness is the #aa_/aeacjjjth
 or #a_/acgedeth part of an ,inch1      
supposing the ,sines are as #aa to #ag4 
,and if this thickness be doubled1 it   
transmits the same bright ,light of the 
second ,ring2 if tripled1 it transmits  
that of the third1 and so on2 the bright
 yellow ,light in all these cases being 
in its ,fits of ,transmission4 ,and     
therefore if its thickness be multiplied
 #cdchf times1 so as to become #a_/d of 
an ,inch1 it transmits the same bright  
,light of the #cdchfth ,ring4 ,suppose  
this be the bright yellow ,light        
transmitted perpendicularly from the    
reflecting convex side of the ,glass    
through the concave side to the white   
,spot in the center of the ,rings of    
,colours on the ,chart3 ,and by a ,rule 
in the #gth and #aith ,observations in  
the first ,part of this ,book1 and by   
the #aeth and #bjth ,propositions of the
 third ,part of this ,book1 if the ,rays

 be made oblique to the ,glass1 the     
thickness of the ,glass requisite to    
transmit the same bright ,light of the  
same ,ring in any obliquity1 is to this 
thickness of #a_/d of an ,inch1 as the  
,secant of a certain ,angle to the      
,radius1 the ,sine of which ,angle is   
the first of an hundred and six         
arithmetical ,means between the ,sines  
of ,incidence and ,refraction1 counted  
from the ,sine of ,incidence when the   
,refraction is made out of any plated   
,body into any ,medium encompassing it2 
that is1 in this case1 out of ,glass    
into ,air4 ,now if the thickness of the 
,glass be increased by degrees1 so as to
 bear to its first thickness1 7viz4 that
 of a quarter of an ,inch17 the         
,proportions which #cdchf 7the number of
 ,fits of the perpendicular ,rays in    
going through the ,glass towards the    
white ,spot in the center of the        
,rings17 hath to #cdche1 #cdchd1 #cdchc1
 and #cdchb1 7the numbers of the ,fits  
of the oblique ,rays in going through   

the ,glass towards the first1 second1   
third1 and fourth ,rings of ,colours17  
and if the first thickness be divided   
into #ajjjjjjjj equal parts1 the        
increased thicknesses will be           
#ajjjjbijh1 #ajjjjehaf1 #ajjjjhgbe1 and 
#ajjjaafcc1 and the ,angles of which    
these thicknesses are ,secants will be  
#bf' #ac''1 #cg' #e''1 #de' #f''1 and   
#eb' #bf''1 the ,radius being           
#ajjjjjjjj2 and the ,sines of these     
,angles are #gfb1 #ajgi1 #acba1 and     
#aebe1 and the proportional ,sines of   
,refraction #aagb1 #afei1 #bjca1 and    
#bcde1 the ,radius being #ajjjjj4 ,for  
since the ,sines of ,incidence out of   
,glass into ,air are to the ,sines of   
,refraction as #aa to #ag1 and to the   
above-mentioned ,secants as #aa to the  
first of #ajf arithmetical ,means       
between #aa and #ag1 that is1 as #aa to 
#aa-f_/ajf1 those ,secants will be to   
the ,sines of ,refraction as #aa-f_/ajf1
 to #ag1 and by this ,analogy will give 
these ,sines4 ,so then1 if the          

obliquities of the ,rays to the concave 
,surface of the ,glass be such that the 
,sines of their ,refraction in passing  
out of the ,glass through that ,surface 
into the ,air be #aagb1 #afei1 #bjca1   
#bcde1 the bright ,light of the #cdchfth
 ,ring shall emerge at the thicknesses  
of the ,glass1 which are to #a_/d of an 
,inch as #cdchf to #cdche1 #cdchd1      
#cdchc1 #cdchb1 respectively4 ,and      
therefore1 if the thickness in all these
 ,cases be #a_/d of an ,inch 7as it is  
in the ,glass of which the ,speculum was
 made7 the bright ,light of the #cdcheth
 ,ring shall emerge where the ,sine of  
,refraction is #aagb1 and that of the   
#cdchdth1 #cdchcth1 and #cdchbth ,ring  
where the ,sine is #afei1 #bjca1 and    
#bcde respectively4 ,and in these       
,angles of ,refraction the ,light of    
these ,rings shall be propagated from   
the ,speculum to the ,chart1 and there  
paint ,rings about the white central    
round ,spot of ,light which we said was 
the ,light of the #cdchfth ,ring4 ,and  

the ,semidiameters of these ,rings shall
 subtend the ,angles of ,refraction made
 at the ,concave-,surface of the        
,speculum1 and by consequence their     
,diameters shall be to the distance of  
the ,chart from the ,speculum as those  
,sines of ,refraction doubled are to the
 ,radius1 that is1 as #aagb1 #afei1     
#bjca1 and #bcde1 doubled are to        
#ajjjjj4 ,and therefore1 if the distance
 of the ,chart from the                 
,concave-,surface of the ,speculum be   
six ,feet 7as it was in the third of    
these ,observations7 the ,diameters of  
the ,rings of this bright yellow ,light 
upon the ,chart shall be #a'fhh1 #b'chi1
 #b'ibe1 #c'cge ,inches3 ,for these     
,diameters are to six ,feet1 as the     
above-mention'd ,sines doubled are to   
the ,radius4 ,now1 these ,diameters of  
the bright yellow ,rings1 thus found by 
,computation are the very same with     
those found in the third of these       
,observations by measuring them1 viz4   
with #a-aa_/af1 #b-c_/h1 #b-aa_/ab1 and 

#c-c_/h ,inches1 and therefore the      
,theory of deriving these ,rings from   
the thickness of the ,plate of ,glass of
 which the ,speculum was made1 and from 
the ,obliquity of the emerging ,rays    
agrees with the ,observation4 ,in this  
,computation ,i have equalled the       
,diameters of the bright ,rings made by 
,light of all ,colours1 to the          
,diameters of the ,rings made by the    
bright yellow4 ,for this yellow makes   
the brightest ,part of the ,rings of all
 ,colours4 ,if you desire the ,diameters
 of the ,rings made by the ,light of any
 other unmix'd ,colour1 you may find    
them readily by putting them to the     
,diameters of the bright yellow ones in 
a subduplicate ,proportion of the       
,intervals of the ,fits of the ,rays of 
those ,colours when equally inclined to 
the refracting or reflecting ,surface   
which caused those ,fits1 that is1 by   
putting the ,diameters of the ,rings    
made by the ,rays in the ,extremities   
and ,limits of the seven ,colours1 red1 

orange1 yellow1 green1 blue1 indigo1    
violet1 proportional to the ,cube-roots 
of the ,numbers1 #a1 #h_/i1 #e_/f1      
#c_/d1 #b_/c1 #c_/e1 #i_/af1 #a_/b1     
which express the ,lengths of a         
,monochord sounding the ,notes in an    
,eighth3 ,for by this means the         
,diameters of the ,rings of these       
,colours will be found pretty nearly in 
the same ,proportion to one another1    
which they ought to have by the fifth of
 these ,observations4  ,and thus ,i     
satisfy'd my self1 that these ,rings    
were of the same kind and ,original with
 those of thin ,plates1 and by          
consequence that the ,fits or alternate 
,dispositions of the ,rays to be        
reflected and transmitted are propagated
 to great distances from every          
reflecting and refracting ,surface4 ,but
 yet to put the matter out of doubt1 ,i 
added the following ,observation4  ,obs4
 #i4 ,if these ,rings thus depend on the
 thickness of the ,plate of ,glass1     
their ,diameters at equal distances from

 several ,speculums made of such        
concavo-convex ,plates of ,glass as are 
ground on the same ,sphere1 ought to be 
reciprocally in a subduplicate          
,proportion of the thicknesses of the   
,plates of ,glass4 ,and if this         
,proportion be found true by experience 
it will amount to a demonstration that  
these ,rings 7like those formed in thin 
,plates7 do depend on the thickness of  
the ,glass4 ,i procured therefore       
another concavo-convex ,plate of ,glass 
ground on both sides to the same ,sphere
 with the former ,plate4 ,its thickness 
was #e_/fb ,parts of an ,inch2 and the  
,diameters of the three first bright    
,rings measured between the brightest   
,parts of their ,orbits at the distance 
of six ,feet from the ,glass were       
#c4d-a_/f4e-a_/h4 ,inches4 ,now1 the    
thickness of the other ,glass being     
#a_/d of an ,inch was to the thickness  
of this ,glass as #a_/d to #e_/fb1 that 
is as #ca to #aj1 or #cajjjjjjj to      
#ajjjjjjjj1 and the ,roots of these     

,numbers are #agfjg and #ajjjj1 and in  
the ,proportion of the first of these   
,roots to the second are the ,diameters 
of the bright ,rings made in this       
,observation by the thinner ,glass1     
#c4d-a_/f4e-a_/h1 to the ,diameters of  
the same ,rings made in the third of    
these ,observations by the thicker      
,glass #a-aa_/af1 #b-c_/h4 #b-aa_/ab1   
that is1 the ,diameters of the ,rings   
are reciprocally in a subduplicate      
,proportion of the thicknesses of the   
,plates of ,glass4  ,so then in ,plates 
of ,glass which are alike concave on one
 side1 and alike convex on the other    
side1 and alike quick-silver'd on the   
convex sides1 and differ in nothing but 
their thickness1 the ,diameters of the  
,rings are reciprocally in a            
subduplicate ,proportion of the         
thicknesses of the ,plates4 ,and this   
shews sufficiently that the ,rings      
depend on both the ,surfaces of the     
,glass4 ,they depend on the convex      
,surface1 because they are more luminous

 when that ,surface is quick-silver'd   
over than when it is without            
,quick-silver4 ,they depend also upon   
the concave ,surface1 because without   
that ,surface a ,speculum makes them    
not4 ,they depend on both ,surfaces1 and
 on the distances between them1 because 
their bigness is varied by varying only 
that distance4 ,and this dependence is  
of the same kind with that which the    
,colours of thin ,plates have on the    
distance of the ,surfaces of those      
,plates1 because the bigness of the     
,rings1 and their ,proportion to one    
another1 and the variation of their     
bigness arising from the variation of   
the thickness of the ,glass1 and the    
,orders of their ,colours1 is such as   
ought to result from the ,propositions  
in the end of the third ,part of this   
,book1 derived from the ,phaenomena of  
the ,colours of thin ,plates set down in
 the first ,part4  ,there are yet other 
,phaenomena of these ,rings of ,colours1
 but such as follow from the same       

,propositions1 and therefore confirm    
both the ,truth of those ,propositions1 
and the ,analogy between these ,rings   
and the ,rings of ,colours made by very 
thin ,plates4 ,i shall subjoin some of  
them4  ,obs4 #aj4 ,when the beam of the 
,sun's ,light was reflected back from   
the ,speculum not directly to the hole  
in the ,window1 but to a place a little 
distant from it1 the common center of   
that ,spot1 and of all the ,rings of    
,colours fell in the middle way between 
the beam of the incident ,light1 and the
 beam of the reflected ,light1 and by   
consequence in the center of the        
spherical concavity of the ,speculum1   
whenever the ,chart on which the ,rings 
of ,colours fell was placed at that     
center4 ,and as the beam of reflected   
,light by inclining the ,speculum       
receded more and more from the beam of  
incident ,light and from the common     
center of the colour'd ,rings between   
them1 those ,rings grew bigger and      
bigger1 and so also did the white round 

,spot1 and new ,rings of ,colours       
emerged successively out of their common
 center1 and the white ,spot became a   
white ,ring encompassing them2 and the  
incident and reflected beams of ,light  
always fell upon the opposite parts of  
this white ,ring1 illuminating its      
,perimeter like two mock ,suns in the   
opposite parts of an ,iris4 ,so then the
 ,diameter of this ,ring1 measured from 
the middle of its ,light on one side to 
the middle of its ,light on the other   
side1 was always equal to the distance  
between the middle of the incident beam 
of ,light1 and the middle of the        
reflected beam measured at the ,chart on
 which the ,rings appeared3 ,and the    
,rays which form'd this ,ring were      
reflected by the ,speculum in ,angles   
equal to their ,angles of ,incidence1   
and by consequence to their ,angles of  
,refraction at their entrance into the  
,glass1 but yet their ,angles of        
,reflexion were not in the same ,planes 
with their ,angles of ,incidence4  ,obs4

 #aa4 ,the ,colours of the new ,rings   
were in a contrary order to those of the
 former1 and arose after this manner4   
,the white round ,spot of ,light in the 
middle of the ,rings continued white to 
the center till the distance of the     
incident and reflected beams at the     
,chart was about #g_/h parts of an      
,inch1 and then it began to grow dark in
 the middle4 ,and when that distance was
 about #a-c_/af of an ,inch1 the white  
,spot was become a ,ring encompassing a 
dark round ,spot which in the middle    
inclined to violet and indigo4 ,and the 
luminous ,rings encompassing it were    
grown equal to those dark ones which in 
the four first ,observations encompassed
 them1 that is to say1 the white ,spot  
was grown a white ,ring equal to the    
first of those dark ,rings1 and the     
first of those luminous ,rings was now  
grown equal to the second of those dark 
ones1 and the second of those luminous  
ones to the third of those dark ones1   
and so on4 ,for the ,diameters of the   

luminous ,rings were now #a-c_/af1      
#b-a_/af1 #b-b_/c1 #c-c_/bj1 c4 ,inches4
  ,when the distance between the        
incident and reflected beams of ,light  
became a little bigger1 there emerged   
out of the middle of the dark ,spot     
after the indigo a blue1 and then out of
 that blue a pale green1 and soon after 
a yellow and red4 ,and when the ,colour 
at the center was brightest1 being      
between yellow and red1 the bright      
,rings were grown equal to those ,rings 
which in the four first ,observations   
next encompassed them2 that is to say1  
the white ,spot in the middle of those  
,rings was now become a white ,ring     
equal to the first of those bright      
,rings1 and the first of those bright   
ones was now become equal to the second 
of those1 and so on4 ,for the ,diameters
 of the white ,ring1 and of the other   
luminous ,rings encompassing it1 were   
now #a-aa_/af1 #b-c_/h1 #b-aa_/ab1      
#c-c_/h1 c4 or thereabouts4  ,when the  
distance of the two beams of ,light at  

the ,chart was a little more increased1 
there emerged out of the middle in order
 after the red1 a purple1 a blue1 a     
green1 a yellow1 and a red inclining    
much to purple1 and when the ,colour was
 brightest being between yellow and red1
 the former indigo1 blue1 green1 yellow 
and red1 were become an ,iris or ,ring  
of ,colours equal to the first of those 
luminous ,rings which appeared in the   
four first ,observations1 and the white 
,ring which was now become the second of
 the luminous ,rings was grown equal to 
the second of those1 and the first of   
those which was now become the third    
,ring was become equal to the third of  
those1 and so on4 ,for their ,diameters 
were #a-aa_/af1 #b-c_/h1 #b-aa_/ab1     
#c-c_/h ,inches1 the distance of the two
 beams of ,light1 and the ,diameter of  
the white ,ring being #b-c_/h ,inches4  
,when these two beams became more       
distant there emerged out of the middle 
of the purplish red1 first a darker     
round ,spot1 and then out of the middle 

of that ,spot a brighter4 ,and now the  
former ,colours 7purple1 blue1 green1   
yellow1 and purplish red7 were become a 
,ring equal to the first of the bright  
,rings mentioned in the four first      
,observations1 and the ,rings about this
 ,ring were grown equal to the ,rings   
about that respectively2 the distance   
between the two beams of ,light and the 
,diameter of the white ,ring 7which was 
now become the third ,ring7 being about 
#c ,inches4  ,the ,colours of the ,rings
 in the middle began now to grow very   
dilute1 and if the distance between the 
two ,beams was increased half an ,inch1 
or an ,inch more1 they vanish'd whilst  
the white ,ring1 with one or two of the 
,rings next it on either side1 continued
 still visible4 ,but if the distance of 
the two beams of ,light was still more  
increased1 these also vanished3 ,for the
 ,light which coming from several parts 
of the hole in the ,window fell upon the
 ,speculum in several ,angles of        
,incidence1 made ,rings of several      

bignesses1 which diluted and blotted out
 one another1 as ,i knew by intercepting
 some part of that ,light4 ,for if ,i   
intercepted that part which was nearest 
to the ,axis of the ,speculum the ,rings
 would be less1 if the other part which 
was remotest from it they would be      
bigger4  ,obs4 #ab4 ,when the ,colours  
of the ,prism were cast successively on 
the ,speculum1 that ,ring which in the  
two last ,observations was white1 was of
 the same bigness in all the ,colours1  
but the ,rings without it were greater  
in the green than in the blue1 and still
 greater in the yellow1 and greatest in 
the red4 ,and1 on the contrary1 the     
,rings within that white ,circle were   
less in the green than in the blue1 and 
still less in the yellow1 and least in  
the red4 ,for the ,angles of ,reflexion 
of those ,rays which made this ,ring1   
being equal to their ,angles of         
,incidence1 the ,fits of every reflected
 ,ray within the ,glass after ,reflexion
 are equal in length and number to the  

,fits of the same ,ray within the ,glass
 before its ,incidence on the reflecting
 ,surface4 ,and therefore since all the 
,rays of all sorts at their entrance    
into the ,glass were in a ,fit of       
,transmission1 they were also in a ,fit 
of ,transmission at their returning to  
the same ,surface after ,reflexion2 and 
by consequence were transmitted1 and    
went out to the white ,ring on the      
,chart4 ,this is the reason why that    
,ring was of the same bigness in all the
 ,colours1 and why in a mixture of all  
it appears white4 ,but in ,rays which   
are reflected in other ,angles1 the     
,intervals of the ,fits of the least    
refrangible being greatest1 make the    
,rings of their ,colour in their        
progress from this white ,ring1 either  
outwards or inwards1 increase or        
decrease by the greatest steps2 so that 
the ,rings of this ,colour without are  
greatest1 and within least4 ,and this is
 the reason why in the last             
,observation1 when the ,speculum was    

illuminated with white ,light1 the      
exterior ,rings made by all ,colours    
appeared red without and blue within1   
and the interior blue without and red   
within4  ,these are the ,phaenomena of  
thick convexo-concave ,plates of ,glass1
 which are every where of the same      
thickness4 ,there are yet other         
,phaenomena when these ,plates are a    
little thicker on one side than on the  
other1 and others when the ,plates are  
more or less concave than convex1 or    
plano-convex1 or double-convex4 ,for in 
all these cases the ,plates make ,rings 
of ,colours1 but after various manners2 
all which1 so far as ,i have yet        
observed1 follow from the ,propositions 
in the end of the third part of this    
,book1 and so conspire to confirm the   
truth of those ,propositions4 ,but the  
,phaenomena are too various1 and the    
,calculations whereby they follow from  
those ,propositions too intricate to be 
here prosecuted4 ,i content my self with
 having prosecuted this kind of         

,phaenomena so far as to discover their 
,cause1 and by discovering it to ratify 
the ,propositions in the third ,part of 
this ,book4  ,obs4 #ac4 ,as ,light      
reflected by a ,lens quick-silver'd on  
the backside makes the ,rings of        
,colours above described1 so it ought to
 make the like ,rings of ,colours in    
passing through a drop of ,water4 ,at   
the first ,reflexion of the ,rays within
 the drop1 some ,colours ought to be    
transmitted1 as in the case of a ,lens1 
and others to be reflected back to the  
,eye4 ,for instance1 if the ,diameter of
 a small drop or globule of ,water be   
about the #ejjth part of an ,inch1 so   
that a red-making ,ray in passing       
through the middle of this globule has  
#bej ,fits of easy ,transmission within 
the globule1 and that all the red-making
 ,rays which are at a certain distance  
from this middle ,ray round about it    
have #bdi ,fits within the globule1 and 
all the like ,rays at a certain farther 
distance round about it have #bdh ,fits1

 and all those at a certain farther     
distance #bdg ,fits1 and so on2 these   
concentrick ,circles of ,rays after     
their transmission1 falling on a white  
,paper1 will make concentrick ,rings of 
red upon the ,paper1 supposing the      
,light which passes through one single  
globule1 strong enough to be sensible4  
,and1 in like manner1 the ,rays of other
 ,colours will make ,rings of other     
,colours4 ,suppose now that in a fair   
,day the ,sun shines through a thin     
,cloud of such globules of ,water or    
,hail1 and that the globules are all of 
the same bigness2 and the ,sun seen     
through this ,cloud shall appear        
encompassed with the like concentrick   
,rings of ,colours1 and the ,diameter of
 the first ,ring of red shall be #g-a_/d
 ,degrees1 that of the second #aj-a_/d  
,degrees1 that of the third #ab ,degrees
 #cc ,minutes4 ,and accordingly as the  
,globules of ,water are bigger or less1 
the ,rings shall be less or bigger4     
,this is the ,theory1 and ,experience   

answers it4 ,for in ,june #afib1 ,i saw 
by reflexion in a ,vessel of stagnating 
,water three ,halos1 ,crowns1 or ,rings 
of ,colours about the ,sun1 like three  
little ,rain-bows1 concentrick to his   
,body4 ,the ,colours of the first or    
innermost ,crown were blue next the     
,sun1 red without1 and white in the     
middle between the blue and red4 ,those 
of the second ,crown were purple and    
blue within1 and pale red without1 and  
green in the middle4 ,and those of the  
third were pale blue within1 and pale   
red without2 these ,crowns enclosed one 
another immediately1 so that their      
,colours proceeded in this continual    
order from the ,sun outward3 blue1      
white1 red2 purple1 blue1 green1 pale   
yellow and red2 pale blue1 pale red4    
,the ,diameter of the second ,crown     
measured from the middle of the yellow  
and red on one side of the ,sun1 to the 
middle of the same ,colour on the other 
side was #i-a_/c ,degrees1 or           
thereabouts4 ,the ,diameters of the     

first and third ,i had not time to      
measure1 but that of the first seemed to
 be about five or six ,degrees1 and that
 of the third about twelve4 ,the like   
,crowns appear sometimes about the      
,moon2 for in the beginning of the ,year
 #affd1 ,febr4 #aith at ,night1 ,i saw  
two such ,crowns about her4 ,the        
,diameter of the first or innermost was 
about three ,degrees1 and that of the   
second about five ,degrees and an half4 
,next about the ,moon was a ,circle of  
white1 and next about that the inner    
,crown1 which was of a bluish green     
within next the white1 and of a yellow  
and red without1 and next about these   
,colours were blue and green on the     
inside of the outward ,crown1 and red on
 the outside of it4 ,at the same time   
there appear'd a ,halo about #bb        
,degrees #ce' distant from the center of
 the ,moon4 ,it was elliptical1 and its 
long ,diameter was perpendicular to the 
,horizon1 verging below farthest from   
the ,moon4 ,i am told that the ,moon has

 sometimes three or more concentrick    
,crowns of ,colours encompassing one    
another next about her ,body4 ,the more 
equal the globules of ,water or ,ice are
 to one another1 the more ,crowns of    
,colours will appear1 and the ,colours  
will be the more lively4 ,the ,halo at  
the distance of #bb-a_/b ,degrees from  
the ,moon is of another sort4 ,by its   
being oval and remoter from the ,moon   
below than above1 ,i conclude1 that it  
was made by ,refraction in some sort of 
,hail or ,snow floating in the ,air in  
an horizontal posture1 the refracting   
,angle being about #eh or #fj ,degrees4 
,,the  ,,third ,,book  ,,of  ,,opticks  
,,part ,i4  ,observations concerning the
 ,inflexions of the ,rays of ,light1 and
 the ,colours made thereby4  ,grimaldo  
has inform'd us1 that if a beam of the  
,sun's ,light be let into a dark ,room  
through a very small hole1 the ,shadows 
of things in this ,light will be larger 
than they ought to be if the ,rays went 
on by the ,bodies in straight ,lines1   

and that these ,shadows have three      
parallel ,fringes1 ,bands or ,ranks of  
colour'd ,light adjacent to them4 ,but  
if the ,hole be enlarged the ,fringes   
grow broad and run into one another1 so 
that they cannot be distinguish'd4      
,these broad ,shadows and ,fringes have 
been reckon'd by some to proceed from   
the ordinary refraction of the ,air1 but
 without due examination of the ,matter4
 ,for the circumstances of the          
,phaenomenon1 so far as ,i have observed
 them1 are as follows4  ,obs4 #a4 ,i    
made in a piece of ,lead a small ,hole  
with a ,pin1 whose breadth was the #db;d
 part of an ,inch4 ,for #ba of those    
,pins laid together took up the breadth 
of half an ,inch4 ,through this ,hole ,i
 let into my darken'd ,chamber a beam of
 the ,sun's ,light1 and found that the  
,shadows of ,hairs1 ,thred1 ,pins1      
,straws1 and such like slender          
,substances placed in this beam of      
,light1 were considerably broader than  
they ought to be1 if the ,rays of ,light

 passed on by these ,bodies in right    
,lines4 ,and particularly a ,hair of a  
,man's ,head1 whose breadth was but the 
#bhjth part of an ,inch1 being held in  
this ,light1 at the distance of about   
twelve ,feet from the ,hole1 did cast a 
,shadow which at the distance of four   
,inches from the ,hair was the sixtieth 
part of an ,inch broad1 that is1 above  
four times broader than the ,hair1 and  
at the distance of two ,feet from the   
,hair was about the eight and twentieth 
part of an ,inch broad1 that is1 ten    
times broader than the ,hair1 and at the
 distance of ten ,feet was the eighth   
part of an ,inch broad1 that is #ce     
times broader4  ,nor is it material     
whether the ,hair be encompassed with   
,air1 or with any other pellucid        
,substance4 ,for ,i wetted a polish'd   
,plate of ,glass1 and laid the ,hair in 
the ,water upon the ,glass1 and then    
laying another polish'd ,plate of ,glass
 upon it1 so that the ,water might fill 
up the space between the ,glasses1 ,i   

held them in the aforesaid beam of      
,light1 so that the ,light might pass   
through them perpendicularly1 and the   
,shadow of the ,hair was at the same    
distances as big as before4 ,the        
,shadows of ,scratches made in polish'd 
,plates of ,glass were also much broader
 than they ought to be1 and the ,veins  
in polish'd ,plates of ,glass did also  
cast the like broad ,shadows4 ,and      
therefore the great breadth of these    
,shadows proceeds from some other cause 
than the ,refraction of the ,air4  ,let 
the ,circle ,x in ,fig4 #a4 represent   
the middle of the ,hair2 ,,adg1 ,,beh1  
,,cfi1 three ,rays passing by one side  
of the ,hair at several distances2      
,,knq1 ,,lor1 ,,mps1 three other ,rays  
passing by the other side of the ,hair  
at the like distances2 ,d1 ,e1 ,f1 and  
,n1 ,o1 ,p1 the places where the ,rays  
are bent in their passage by the ,hair2 
,g1 ,h1 ,i1 and ,q1 ,r1 ,s1 the places  
where the ,rays fall on a ,paper ,,gq2  
,,is the breadth of the ,shadow of the  

,hair cast on the ,paper1 and ,,ti1     
,,vs1 two ,rays passing to the ,points  
,i and ,s without bending when the ,hair
 is taken away4 ,and it's manifest that 
all the ,light between these two ,rays  
,,ti and ,,vs is bent in passing by the 
,hair1 and turned aside from the ,shadow
 ,,is1 because if any part of this      
,light were not bent it would fall on   
the ,paper within the ,shadow1 and there
 illuminate the ,paper1 contrary to     
experience4 ,and because when the ,paper
 is at a great distance from the ,hair1 
the ,shadow is broad1 and therefore the 
,rays ,,ti and ,,vs are at a great      
distance from one another1 it follows   
that the ,hair acts upon the ,rays of   
,light at a good distance in their      
passing by it4 ,but the ,action is      
strongest on the ,rays which pass by at 
least distances1 and grows weaker and   
weaker accordingly as the ,rays pass by 
at distances greater and greater1 as is 
represented in the ,scheme3 ,for thence 
it comes to pass1 that the ,shadow of   

the ,hair is much broader in proportion 
to the distance of the ,paper from the  
,hair1 when the ,paper is nearer the    
,hair1 than when it is at a great       
distance from it4  ,obs4 #b4 ,the       
,shadows of all ,bodies 7,metals1       
,stones1 ,glass1 ,wood1 ,horn1 ,ice1 c47
 in this ,light were border'd with three
 ,parallel ,fringes or ,bands of        
colour'd ,light1 whereof that which was 
contiguous to the ,shadow was broadest  
and most luminous1 and that which was   
remotest from it was narrowest1 and so  
faint1 as not easily to be visible4 ,it 
was difficult to distinguish the        
,colours1 unless when the ,light fell   
very obliquely upon a smooth ,paper1 or 
some other smooth white ,body1 so as to 
make them appear much broader than they 
would otherwise do4 ,and then the       
,colours were plainly visible in this   
,order3 ,the first or innermost ,fringe 
was violet and deep blue next the       
,shadow1 and then light blue1 green1 and
 yellow in the middle1 and red without4 

,the second ,fringe was almost          
contiguous to the first1 and the third  
to the second1 and both were blue       
within1 and yellow and red without1 but 
their ,colours were very faint1         
especially those of the third4 ,the     
,colours therefore proceeded in this    
order from the ,shadow2 violet1 indigo1 
pale blue1 green1 yellow1 red2 blue1    
yellow1 red2 pale blue1 pale yellow and 
red4 ,the ,shadows made by ,scratches   
and ,bubbles in polish'd ,plates of     
,glass were border'd with the like      
,fringes of colour'd ,light4 ,and if    
,plates of ,looking-glass sloop'd off   
near the edges with a ,diamond-cut1 be  
held in the same beam of ,light1 the    
,light which passes through the parallel
 ,planes of the ,glass will be border'd 
with the like ,fringes of ,colours where
 those ,planes meet with the            
,diamond-cut1 and by this means there   
will sometimes appear four or five      
,fringes of ,colours4 ,let ,,ab1 ,,cd in
 ,fig4 #b4 represent the parallel       

,planes of a ,looking-glass1 and ,,bd   
the ,plane of the ,diamond-cut1 making  
at ,b a very obtuse ,angle with the     
,plane ,,ab4 ,and let all the ,light    
between the ,rays ,,eni and ,,fbm pass  
directly through the parallel ,planes of
 the ,glass1 and fall upon the ,paper   
between ,i and ,m1 and all the ,light   
between the ,rays ,,go and ,,hd be      
refracted by the oblique ,plane of the  
,diamond-cut ,,bd1 and fall upon the    
,paper between ,k and ,l2 and the ,light
 which passes directly through the      
parallel ,planes of the ,glass1 and     
falls upon the ,paper between ,i and ,m1
 will be border'd with three or more    
,fringes at ,m4  ,illustration3 ,,fig4  
#a4  ,illustration3 ,,fig4 #b4  ,so by  
looking on the ,sun through a ,feather  
or black ,ribband held close to the     
,eye1 several ,rain-bows will appear2   
the ,shadows which the ,fibres or       
,threds cast on the ,tunica ,retina1    
being border'd with the like ,fringes of
 ,colours4  ,obs4 #c4 ,when the ,hair   

was twelve ,feet distant from this      
,hole1 and its ,shadow fell obliquely   
upon a flat white ,scale of ,inches and 
,parts of an ,inch placed half a ,foot  
beyond it1 and also when the ,shadow    
fell perpendicularly upon the same      
,scale placed nine ,feet beyond it2 ,i  
measured the breadth of the ,shadow and 
,fringes as accurately as ,i could1 and 
found them in ,parts of an ,inch as     
follows4                                
----------------------------------------
----------------------                  
half a    ,nine                         
,at the ,distance of      ,foot         
,feet                                   
----------------------------------------
---------------------- ,the breadth of  
the ,shadow                     #a_/ed  
#a_/i                                   
----------------------------------------
---------------------- ,the breadth     
between the ,middles of the             
#a_/ch       brightest ,light of the    
innermost ,fringes     or        on     

either side the ,shadow                 
#a_/ci      #g_/ej                      
----------------------------------------
---------------------- ,the breadth     
between the ,middles of the             
brightest ,light of the middlemost      
,fringes              on either side the
 ,shadow                 #a_/bc-a_/b    
#d_/ag                                  
----------------------------------------
---------------------- ,the breadth     
between the ,middles of the       #a_/ah
        brightest ,light of the outmost 
,fringes      or         on either side 
the ,shadow                 #a_/ah-a_/b 
#c_/aj                                  
----------------------------------------
---------------------- ,the distance    
between the ,middles of the             
brightest ,light of the first and second
                ,fringes                
#a_/abj      #a_/ba                     
----------------------------------------
---------------------- ,the distance    
between the ,middles of the             

brightest ,light of the second and third
                ,fringes                
#a_/agj      #a_/ca                     
----------------------------------------
---------------------- ,the breadth of  
the luminous ,part 7green1              
white1 yellow1 and red7 of the first    
,fringe                                 
#a_/agj      #a_/cb                     
----------------------------------------
---------------------- ,the breadth of  
the darker ,space between               
the first and second ,fringes           
#a_/bdj      #a_/de                     
----------------------------------------
---------------------- ,the breadth of  
the luminous ,part of the               
second ,fringe                          
#a_/bij      #a_/ee                     
----------------------------------------
---------------------- ,the breadth of  
the darker ,space between               
the second and third ,fringes           
#a_/cdj      #a_/fc                     
----------------------------------------

----------------------  ,these ,measures
 ,i took by letting the ,shadow of the  
,hair1 at half a ,foot distance1 fall so
 obliquely on the ,scale1 as to appear  
twelve times broader than when it fell  
perpendicularly on it at the same       
distance1 and setting down in this      
,table the twelfth part of the ,measures
 ,i then took4  ,obs4 #d4 ,when the     
,shadow and ,fringes were cast obliquely
 upon a smooth white ,body1 and that    
,body was removed farther and farther   
from the ,hair1 the first ,fringe began 
to appear and look brighter than the    
rest of the ,light at the distance of   
less than a quarter of an ,inch from the
 ,hair1 and the dark ,line or ,shadow   
between that and the second ,fringe     
began to appear at a less distance from 
the ,hair than that of the third part of
 an ,inch4 ,the second ,fringe began to 
appear at a distance from the ,hair of  
less than half an ,inch1 and the ,shadow
 between that and the third ,fringe at a
 distance less than an inch1 and the    

third ,fringe at a distance less than   
three ,inches4 ,at greater distances    
they became much more sensible1 but kept
 very nearly the same proportion of     
their breadths and intervals which they 
had at their first appearing4 ,for the  
distance between the middle of the      
first1 and middle of the second ,fringe1
 was to the distance between the middle 
of the second and middle of the third   
,fringe1 as three to two1 or ten to     
seven4 ,and the last of these two       
distances was equal to the breadth of   
the bright ,light or luminous part of   
the first ,fringe4 ,and this breadth was
 to the breadth of the bright ,light of 
the second ,fringe as seven to four1 and
 to the dark ,interval of the first and 
second ,fringe as three to two1 and to  
the like dark ,interval between the     
second and third as two to one4 ,for the
 breadths of the ,fringes seem'd to be  
in the progression of the ,numbers #a1  
sqrt7#a_/c71 sqrt7#a_/e71 and their     
,intervals to be in the same progression

 with them2 that is1 the ,fringes and   
their ,intervals together to be in the  
continual progression of the ,numbers   
#a1 sqrt7#a_/b71 sqrt7#a_/c71           
sqrt7#a_/d71 sqrt7#a_/e71 or            
thereabouts4 ,and these ,proportions    
held the same very nearly at all        
distances from the ,hair2 the dark      
,intervals of the ,fringes being as     
broad in proportion to the breadth of   
the ,fringes at their first appearance  
as afterwards at great distances from   
the ,hair1 though not so dark and       
distinct4  ,obs4 #e4 ,the ,sun shining  
into my darken'd ,chamber through a hole
 a quarter of an ,inch broad1 ,i placed 
at the distance of two or three ,feet   
from the ,hole a ,sheet of ,pasteboard1 
which was black'd all over on both      
sides1 and in the middle of it had a    
hole about three quarters of an ,inch   
square for the ,light to pass through4  
,and behind the hole ,i fasten'd to the 
,pasteboard with ,pitch the blade of a  
sharp ,knife1 to intercept some part of 

the ,light which passed through the     
hole4 ,the ,planes of the ,pasteboard   
and blade of the ,knife were parallel to
 one another1 and perpendicular to the  
,rays4 ,and when they were so placed    
that none of the ,sun's ,light fell on  
the ,pasteboard1 but all of it passed   
through the hole to the ,knife1 and     
there part of it fell upon the blade of 
the ,knife1 and part of it passed by its
 edge2 ,i let this part of the ,light   
which passed by1 fall on a white ,paper 
two or three ,feet beyond the ,knife1   
and there saw two streams of faint      
,light shoot out both ways from the beam
 of ,light into the shadow1 like the    
,tails of ,comets4 ,but because the     
,sun's direct ,light by its brightness  
upon the ,paper obscured these faint    
streams1 so that ,i could scarce see    
them1 ,i made a little hole in the midst
 of the ,paper for that ,light to pass  
through and fall on a black ,cloth      
behind it2 and then ,i saw the two      
streams plainly4 ,they were like one    

another1 and pretty nearly equal in     
length1 and breadth1 and quantity of    
,light4 ,their ,light at that end next  
the ,sun's direct ,light was pretty     
strong for the space of about a quarter 
of an ,inch1 or half an ,inch1 and in   
all its progress from that direct ,light
 decreased gradually till it became     
insensible4 ,the whole length of either 
of these streams measured upon the paper
 at the distance of three ,feet from the
 ,knife was about six or eight ,inches2 
so that it subtended an ,angle at the   
edge of the ,knife of about #aj or #ab1 
or at most #ad ,degrees4 ,yet sometimes 
,i thought ,i saw it shoot three or four
 ,degrees farther1 but with a ,light so 
very faint that ,i could scarce perceive
 it1 and suspected it might 7in some    
measure at least7 arise from some other 
cause than the two streams did4 ,for    
placing my ,eye in that ,light beyond   
the end of that stream which was behind 
the ,knife1 and looking towards the     
,knife1 ,i could see a line of ,light   

upon its edge1 and that not only when my
 ,eye was in the line of the ,streams1  
but also when it was without that line  
either towards the point of the ,knife1 
or towards the handle4 ,this line of    
,light appear'd contiguous to the edge  
of the ,knife1 and was narrower than the
 ,light of the innermost ,fringe1 and   
narrowest when my ,eye was farthest from
 the direct ,light1 and therefore seem'd
 to pass between the ,light of that     
,fringe and the edge of the ,knife1 and 
that which passed nearest the edge to be
 most bent1 though not all of it4  ,obs4
 #f4 ,i placed another ,knife by this1  
so that their edges might be parallel1  
and look towards one another1 and that  
the beam of ,light might fall upon both 
the ,knives1 and some part of it pass   
between their edges4 ,and when the      
distance of their edges was about the   
#djjth part of an ,inch1 the stream     
parted in the middle1 and left a ,shadow
 between the two parts4 ,this ,shadow   
was so black and dark that all the      

,light which passed between the ,knives 
seem'd to be bent1 and turn'd aside to  
the one hand or to the other4 ,and as   
the ,knives still approach'd one another
 the ,shadow grew broader1 and the      
streams shorter at their inward ends    
which were next the ,shadow1 until upon 
the contact of the ,knives the whole    
,light vanish'd1 leaving its place to   
the ,shadow4  ,and hence ,i gather that 
the ,light which is least bent1 and goes
 to the inward ends of the streams1     
passes by the edges of the ,knives at   
the greatest distance1 and this distance
 when the ,shadow begins to appear      
between the streams1 is about the #hjjth
 part of an ,inch4 ,and the ,light which
 passes by the edges of the ,knives at  
distances still less and less1 is more  
and more bent1 and goes to those parts  
of the streams which are farther and    
farther from the direct ,light2 because 
when the ,knives approach one another   
till they touch1 those parts of the     
streams vanish last which are farthest  

from the direct ,light4  ,obs4 #g4 ,in  
the fifth ,observation the ,fringes did 
not appear1 but by reason of the breadth
 of the hole in the ,window became so   
broad as to run into one another1 and by
 joining1 to make one continued ,light  
in the beginning of the streams4 ,but in
 the sixth1 as the ,knives approached   
one another1 a little before the ,shadow
 appeared between the two streams1 the  
,fringes began to appear on the inner   
ends of the ,streams on either side of  
the direct ,light2 three on one side    
made by the edge of one ,knife1 and     
three on the other side made by the edge
 of the other ,knife4 ,they were        
distinctest when the ,knives were placed
 at the greatest distance from the hole 
in the ,window1 and still became more   
distinct by making the hole less1       
insomuch that ,i could sometimes see a  
faint lineament of a fourth ,fringe     
beyond the three above mention'd4 ,and  
as the ,knives continually approach'd   
one another1 the ,fringes grew          

distincter and larger1 until they       
vanish'd4 ,the outmost ,fringe vanish'd 
first1 and the middlemost next1 and the 
innermost last4 ,and after they were all
 vanish'd1 and the line of ,light which 
was in the middle between them was grown
 very broad1 enlarging it self on both  
sides into the streams of ,light        
described in the fifth ,observation1 the
 above-mention'd ,shadow began to appear
 in the middle of this line1 and divide 
it along the middle into two lines of   
,light1 and increased until the whole   
,light vanish'd4 ,this enlargement of   
the ,fringes was so great that the ,rays
 which go to the innermost ,fringe      
seem'd to be bent above twenty times    
more when this ,fringe was ready to     
vanish1 than when one of the ,knives was
 taken away4  ,and from this and the    
former ,observation compared1 ,i gather1
 that the ,light of the first ,fringe   
passed by the edge of the ,knife at a   
distance greater than the #hjjth part of
 an ,inch1 and the ,light of the second 

,fringe passed by the edge of the ,knife
 at a greater distance than the ,light  
of the first ,fringe did1 and that of   
the third at a greater distance than    
that of the second1 and that of the     
streams of ,light described in the fifth
 and sixth ,observations passed by the  
edges of the ,knives at less distances  
than that of any of the ,fringes4  ,obs4
 #h4 ,i caused the edges of two ,knives 
to be ground truly strait1 and pricking 
their points into a ,board so that their
 edges might look towards one another1  
and meeting near their points contain a 
rectilinear ,angle1 ,i fasten'd their   
,handles together with ,pitch to make   
this ,angle invariable4 ,the distance of
 the edges of the ,knives from one      
another at the distance of four ,inches 
from the angular ,point1 where the edges
 of the ,knives met1 was the eighth part
 of an ,inch2 and therefore the ,angle  
contain'd by the edges was about one    
,degree #ed3 ,the ,knives thus fix'd    
together ,i placed in a beam of the     

,sun's ,light1 let into my darken'd     
,chamber through a ,hole the #db;d ,part
 of an ,inch wide1 at the distance of   
#aj or #ae ,feet from the ,hole1 and let
 the ,light which passed between their  
edges fall very obliquely upon a smooth 
white ,ruler at the distance of half an 
,inch1 or an ,inch from the ,knives1 and
 there saw the ,fringes by the two edges
 of the ,knives run along the edges of  
the ,shadows of the ,knives in ,lines   
parallel to those edges without growing 
sensibly broader1 till they met in      
,angles equal to the ,angle contained by
 the edges of the ,knives1 and where    
they met and joined they ended without  
crossing one another4 ,but if the ,ruler
 was held at a much greater distance    
from the ,knives1 the ,fringes where    
they were farther from the ,place of    
their ,meeting1 were a little narrower1 
and became something broader and broader
 as they approach'd nearer and nearer to
 one another1 and after they met they   
cross'd one another1 and then became    

much broader than before4  ,whence ,i   
gather that the distances at which the  
,fringes pass by the ,knives are not    
increased nor alter'd by the approach of
 the ,knives1 but the ,angles in which  
the ,rays are there bent are much       
increased by that approach2 and that the
 ,knife which is nearest any ,ray       
determines which way the ,ray shall be  
bent1 and the other ,knife increases the
 bent4  ,obs4 #i4 ,when the ,rays fell  
very obliquely upon the ,ruler at the   
distance of the third ,part of an ,inch 
from the ,knives1 the dark ,line between
 the first and second ,fringe of the    
,shadow of one ,knife1 and the dark     
,line between the first and second      
,fringe of the ,shadow of the other     
knife met with one another1 at the      
distance of the fifth ,part of an ,inch 
from the end of the ,light which passed 
between the ,knives at the concourse of 
their edges4 ,and therefore the distance
 of the edges of the ,knives at the     
meeting of these dark ,lines was the    

#afjth ,part of an ,inch4 ,for as four  
,inches to the eighth ,part of an ,inch1
 so is any ,length of the edges of the  
,knives measured from the point of their
 concourse to the distance of the edges 
of the ,knives at the end of that       
,length1 and so is the fifth ,part of an
 ,inch to the #afjth ,part4 ,so then the
 dark ,lines above-mention'd meet in the
 middle of the ,light which passes      
between the ,knives where they are      
distant the #afjth ,part of an ,inch1   
and the one half of that ,light passes  
by the edge of one ,knife at a distance 
not greater than the #cbjth ,part of an 
,inch1 and falling upon the ,paper makes
 the ,fringes of the ,shadow of that    
,knife1 and the other half passes by the
 edge of the other ,knife1 at a distance
 not greater than the #cbjth ,part of an
 ,inch1 and falling upon the ,paper     
makes the ,fringes of the ,shadow of the
 other ,knife4 ,but if the ,paper be    
held at a distance from the ,knives     
greater than the third ,part of an      

,inch1 the dark ,lines above-mention'd  
meet at a greater distance than the     
fifth ,part of an ,inch from the end of 
the ,light which passed between the     
,knives at the concourse of their edges2
 and therefore the ,light which falls   
upon the ,paper where those dark ,lines 
meet passes between the ,knives where   
the edges are distant above the #afjth  
part of an ,inch4  ,for at another time1
 when the two ,knives were distant eight
 ,feet and five ,inches from the little 
hole in the ,window1 made with a small  
,pin as above1 the ,light which fell    
upon the ,paper where the aforesaid dark
 lines met1 passed between the ,knives1 
where the distance between their edges  
was as in the following ,table1 when the
 distance of the ,paper from the ,knives
 was also as follows4                   
----------------------------------------
-------------------                     
,distances between the edges  ,distances
 of the ,paper        of the ,knives in 
millesimal  from the ,knives in ,inches4

        parts of an ,inch4              
----------------------------------------
-------------------           #a-a_/b4  
#j'jab           #c-a_/c4               
#j'jbj           #h-c_/e4               
#j'jcd          #cb4                    
#j'jeg          #if4                    
#j'jha         #aca4                    
#j'jhg   ,and hence ,i gather1 that the 
,light which makes the ,fringes upon the
 ,paper is not the same ,light at all   
distances of the ,paper from the        
,knives1 but when the ,paper is held    
near the ,knives1 the ,fringes are made 
by ,light which passes by the edges of  
the ,knives at a less distance1 and is  
more bent than when the ,paper is held  
at a greater distance from the ,knives4 
,illustration3 ,,fig4 #c4  ,obs4 #aj4   
,when the ,fringes of the ,shadows of   
the ,knives fell perpendicularly upon a 
,paper at a great distance from the     
,knives1 they were in the form of       
,hyperbola's1 and their ,dimensions were
 as follows4 ,let ,,ca1 ,,cb in ,fig4   

#c4 represent ,lines drawn upon the     
,paper parallel to the edges of the     
,knives1 and between which all the      
,light would fall1 if it passed between 
the edges of the ,knives without        
inflexion2 ,,de a ,right ,line drawn    
through ,c making the ,angles ,,acd1    
,,bce1 equal to one another1 and        
terminating all the ,light which falls  
upon the ,paper from the point where the
 edges of the ,knives meet2 eis1 fkt1   
and glv1 three hyperbolical ,lines      
representing the ,terminus of the       
,shadow of one of the ,knives1 the dark 
,line between the first and second      
,fringes of that ,shadow1 and the dark  
,line between the second and third      
,fringes of the same ,shadow2 xip1 ykq1 
and zlr1 three other hyperbolical ,lines
 representing the ,terminus of the      
,shadow of the other ,knife1 the dark   
,line between the first and second      
,fringes of that ,shadow1 and the dark  
line between the second and third       
,fringes of the same ,shadow4 ,and      

conceive that these three ,hyperbola's  
are like and equal to the former three1 
and cross them in the points i1 k1 and  
l1 and that the ,shadows of the ,knives 
are terminated and distinguish'd from   
the first luminous ,fringes by the lines
 eis and xip1 until the meeting and     
crossing of the ,fringes1 and then those
 lines cross the ,fringes in the form of
 dark lines1 terminating the first      
luminous ,fringes within side1 and      
distinguishing them from another ,light 
which begins to appear at i1 and        
illuminates all the triangular space    
ip,,des comprehended by these dark      
lines1 and the right line ,,de4 ,of     
these ,hyperbola's one ,asymptote is the
 line ,,de1 and their other ,asymptotes 
are parallel to the lines ,,ca and ,,cb4
 ,let rv represent a line drawn any     
where upon the ,paper parallel to the   
,asymptote ,,de1 and let this line cross
 the right lines ,,ac in m1 and ,,bc in 
n1 and the six dark hyperbolical lines  
in p1 q1 r2 s1 t1 v2 and by measuring   

the distances ps1 qt1 rv1 and thence    
collecting the lengths of the ,ordinates
 np1 nq1 nr or ms1 mt1 mv1 and doing    
this at several distances of the line rv
 from the ,asymptote ,,dd1 you may find 
as many points of these ,hyperbola's as 
you please1 and thereby know that these 
curve lines are ,hyperbola's differing  
little from the conical ,hyperbola4 ,and
 by measuring the lines ,ci1 ,ck1 ,cl1  
you may find other points of these      
,curves4  ,for instance2 when the       
,knives were distant from the hole in   
the ,window ten ,feet1 and the ,paper   
from the ,knives nine ,feet1 and the    
,angle contained by the edges of the    
,knives to which the ,angle ,,acb is    
equal1 was subtended by a ,chord which  
was to the ,radius as #a to #cb1 and the
 distance of the line rv from the       
,asymptote ,,de was half an ,inch3 ,i   
measured the lines ps1 qt1 rv1 and found
 them #j'ce1 #j'fe1 #j'ih ,inches       
respectively2 and by adding to their    
halfs the line #a_/b mn1 7which here was

 the #abhth part of an ,inch1 or #j'jjgh
 ,inches17 the ,sums np1 nq1 nr1 were   
#j'ahbh1 #j'ccbh1 #j'digh ,inches4 ,i   
measured also the distances of the      
brightest parts of the ,fringes which   
run between pq and st1 qr and tv1 and   
next beyond r and v1 and found them     
#j'e1 #j'h1 and #a'ag ,inches4  ,obs4   
#aa4 ,the ,sun shining into my darken'd 
,room through a small round hole made in
 a ,plate of ,lead with a slender ,pin1 
as above2 ,i placed at the hole a ,prism
 to refract the ,light1 and form on the 
opposite ,wall the ,spectrum of         
,colours1 described in the third        
,experiment of the first ,book4 ,and    
then ,i found that the ,shadows of all  
,bodies held in the colour'd ,light     
between the ,prism and the ,wall1 were  
border'd with ,fringes of the ,colour of
 that ,light in which they were held4   
,in the full red ,light they were       
totally red without any sensible blue or
 violet1 and in the deep blue ,light    
they were totally blue without any      

sensible red or yellow2 and so in the   
green ,light they were totally green1   
excepting a little yellow and blue1     
which were mixed in the green ,light of 
the ,prism4 ,and comparing the ,fringes 
made in the several colour'd ,lights1 ,i
 found that those made in the red ,light
 were largest1 those made in the violet 
were least1 and those made in the green 
were of a middle bigness4 ,for the      
,fringes with which the ,shadow of a    
,man's ,hair were bordered1 being       
measured cross the ,shadow at the       
distance of six ,inches from the ,hair1 
the distance between the middle and most
 luminous part of the first or innermost
 ,fringe on one side of the ,shadow1 and
 that of the like ,fringe on the other  
side of the ,shadow1 was in the full red
 ,light #a_/cg-a_/d of an ,inch1 and in 
the full violet #g_/df4 ,and the like   
distance between the middle and most    
luminous parts of the second ,fringes on
 either side the ,shadow was in the full
 red ,light #a_/bb1 and in the violet   

#a_/bg of an ,inch4 ,and these distances
 of the ,fringes held the same          
proportion at all distances from the    
,hair without any sensible variation4   
,so then the ,rays which made these     
,fringes in the red ,light passed by the
 ,hair at a greater distance than those 
did which made the like ,fringes in the 
violet2 and therefore the ,hair in      
causing these ,fringes acted alike upon 
the red ,light or least refrangible     
,rays at a greater distance1 and upon   
the violet or most refrangible ,rays at 
a less distance1 and by those actions   
disposed the red ,light into ,larger    
,fringes1 and the violet into smaller1  
and the ,lights of intermediate ,colours
 into ,fringes of intermediate bignesses
 without changing the ,colour of any    
sort of ,light4  ,when therefore the    
,hair in the first and second of these  
,observations was held in the white beam
 of the ,sun's ,light1 and cast a       
,shadow which was border'd with three   
,fringes of coloured ,light1 those      

,colours arose not from any new         
modifications impress'd upon the ,rays  
of ,light by the ,hair1 but only from   
the various inflexions whereby the      
several ,sorts of ,rays were separated  
from one another1 which before          
separation1 by the mixture of all their 
,colours1 composed the white beam of the
 ,sun's ,light1 but whenever separated  
compose ,lights of the several ,colours 
which they are originally disposed to   
exhibit4 ,in this #aath ,observation1   
where the ,colours are separated before 
the ,light passes by the ,hair1 the     
least refrangible ,rays1 which when     
separated from the rest make red1 were  
inflected at a greater distance from the
 ,hair1 so as to make three red ,fringes
 at a greater distance from the middle  
of the ,shadow of the ,hair2 and the    
most refrangible ,rays which when       
separated make violet1 were inflected at
 a less distance from the ,hair1 so as  
to make three violet ,fringes at a less 
distance from the middle of the ,shadow 

of the ,hair4 ,and other ,rays of       
intermediate degrees of ,refrangibility 
were inflected at intermediate distances
 from the ,hair1 so as to make ,fringes 
of intermediate ,colours at intermediate
 distances from the middle of the       
,shadow of the ,hair4 ,and in the second
 ,observation1 where all the ,colours   
are mix'd in the white ,light which     
passes by the ,hair1 these ,colours are 
separated by the various inflexions of  
the ,rays1 and the ,fringes which they  
make appear all together1 and the       
innermost ,fringes being contiguous make
 one broad ,fringe composed of all the  
,colours in due order1 the violet lying 
on the inside of the ,fringe next the   
,shadow1 the red on the outside farthest
 from the ,shadow1 and the blue1 green1 
and yellow1 in the middle4 ,and1 in like
 manner1 the middlemost ,fringes of all 
the ,colours lying in order1 and being  
contiguous1 make another broad ,fringe  
composed of all the ,colours2 and the   
outmost ,fringes of all the ,colours    

lying in order1 and being contiguous1   
make a third broad ,fringe composed of  
all the ,colours4 ,these are the three  
,fringes of colour'd ,light with which  
the ,shadows of all ,bodies are border'd
 in the second ,observation4  ,when ,i  
made the foregoing ,observations1 ,i    
design'd to repeat most of them with    
more care and exactness1 and to make    
some new ones for determining the manner
 how the ,rays of ,light are bent in    
their passage by ,bodies1 for making the
 ,fringes of ,colours with the dark     
lines between them4 ,but ,i was then    
interrupted1 and cannot now think of    
taking these things into farther        
,consideration4 ,and since ,i have not  
finish'd this part of my ,design1 ,i    
shall conclude with proposing only some 
,queries1 in order to a farther search  
to be made by others4  ,query #a4 ,do   
not ,bodies act upon ,light at a        
distance1 and by their action bend its  
,rays2 and is not this action 7caeteris 
paribus7 strongest at the least         

distance8  ,qu4 #b4 ,do not the ,rays   
which differ in ,refrangibility differ  
also in ,flexibity2 and are they not by 
their different ,inflexions separated   
from one another1 so as after separation
 to make the ,colours in the three      
,fringes above described8 ,and after    
what manner are they inflected to make  
those ,fringes8  ,qu4 #c4 ,are not the  
,rays of ,light in passing by the edges 
and sides of ,bodies1 bent several times
 backwards and forwards1 with a motion  
like that of an ,eel8 ,and do not the   
three ,fringes of colour'd ,light       
above-mention'd arise from three such   
bendings8  ,qu4 #d4 ,do not the ,rays of
 ,light which fall upon ,bodies1 and are
 reflected or refracted1 begin to bend  
before they arrive at the ,bodies2 and  
are they not reflected1 refracted1 and  
inflected1 by one and the same          
,principle1 acting variously in various 
,circumstances8  ,qu4 #e4 ,do not       
,bodies and ,light act mutually upon one
 another2 that is to say1 ,bodies upon  

,light in emitting1 reflecting1         
refracting and inflecting it1 and ,light
 upon ,bodies for heating them1 and     
putting their parts into a vibrating    
motion wherein heat consists8  ,qu4 #f4 
,do not black ,bodies conceive heat more
 easily from ,light than those of other 
,colours do1 by reason that the ,light  
falling on them is not reflected        
outwards1 but enters the ,bodies1 and is
 often reflected and refracted within   
them1 until it be stifled and lost8     
,qu4 #g4 ,is not the strength and vigor 
of the action between ,light and        
sulphureous ,bodies observed above1 one 
reason why sulphureous ,bodies take fire
 more readily1 and burn more vehemently 
than other ,bodies do8  ,qu4 #h4 ,do not
 all fix'd ,bodies1 when heated beyond a
 certain degree1 emit ,light and shine2 
and is not this ,emission perform'd by  
the vibrating motions of their parts8   
,and do not all ,bodies which abound    
with terrestrial parts1 and especially  
with sulphureous ones1 emit ,light as   

often as those parts are sufficiently   
agitated2 whether that agitation be made
 by ,heat1 or by ,friction1 or          
,percussion1 or ,putrefaction1 or by any
 vital ,motion1 or any other ,cause8 ,as
 for instance2 ,sea-,water in a raging  
,storm2 ,quick-silver agitated in vacuo2
 the ,back of a ,cat1 or ,neck of a     
,horse1 obliquely struck or rubbed in a 
dark place2 ,wood1 ,flesh and ,fish     
while they putrefy2 ,vapours arising    
from putrefy'd ,waters1 usually call'd  
,ignes ,fatui2 ,stacks of moist ,hay or 
,corn growing hot by fermentation2      
,glow-worms and the ,eyes of some       
,animals by vital ,motions2 the vulgar  
,phosphorus agitated by the attrition of
 any ,body1 or by the acid ,particles of
 the ,air2 ,amber and some ,diamonds by 
striking1 pressing or rubbing them2     
,scrapings of ,steel struck off with a  
,flint2 ,iron hammer'd very nimbly till 
it become so hot as to kindle ,sulphur  
thrown upon it2 the ,axletrees of       
,chariots taking fire by the rapid      

rotation of the ,wheels2 and some       
,liquors mix'd with one another whose   
,particles come together with an        
,impetus1 as ,oil of ,vitriol distilled 
from its weight of ,nitre1 and then     
mix'd with twice its weight of ,oil of  
,anniseeds4 ,so also a ,globe of ,glass 
about #h or #aj ,inches in diameter1    
being put into a ,frame where it may be 
swiftly turn'd round its ,axis1 will in 
turning shine where it rubs against the 
palm of ones ,hand apply'd to it3 ,and  
if at the same time a piece of white    
,paper or white ,cloth1 or the end of   
ones ,finger be held at the distance of 
about a quarter of an ,inch or half an  
,inch from that part of the ,glass where
 it is most in motion1 the electrick    
,vapour which is excited by the friction
 of the ,glass against the ,hand1 will  
by dashing against the white ,paper1    
,cloth or ,finger1 be put into such an  
agitation as to emit ,light1 and make   
the white ,paper1 ,cloth or ,finger1    
appear lucid like a ,glowworm2 and in   

rushing out of the ,glass will sometimes
 push against the finger so as to be    
felt4 ,and the same things have been    
found by rubbing a long and large       
,cylinder or ,glass or ,amber with a    
,paper held in ones hand1 and continuing
 the friction till the ,glass grew warm4
  ,qu4 #i4 ,is not ,fire a ,body heated 
so hot as to emit ,light copiously8 ,for
 what else is a red hot ,iron than      
,fire8 ,and what else is a burning ,coal
 than red hot ,wood8  ,qu4 #aj4 ,is not 
,flame a ,vapour1 ,fume or ,exhalation  
heated red hot1 that is1 so hot as to   
shine8 ,for ,bodies do not flame without
 emitting a copious ,fume1 and this     
,fume burns in the ,flame4 ,the ,ignis  
,fatuus is a ,vapour shining without    
heat1 and is there not the same         
difference between this ,vapour and     
,flame1 as between rotten ,wood shining 
without heat and burning ,coals of      
,fire8 ,in distilling hot ,spirits1 if  
the ,head of the ,still be taken off1   
the ,vapour which ascends out of the    

,still will take fire at the ,flame of a
 ,candle1 and turn into ,flame1 and the 
,flame will run along the ,vapour from  
the ,candle to the ,still4 ,some ,bodies
 heated by ,motion1 or ,fermentation1 if
 the heat grow intense1 fume copiously1 
and if the heat be great enough the     
,fumes will shine and become ,flame4    
,metals in fusion do not flame for want 
of a copious ,fume1 except ,spelter1    
which fumes copiously1 and thereby      
flames4 ,all flaming ,bodies1 as ,oil1  
,tallow1 ,wax1 ,wood1 fossil ,coals1    
,pitch1 ,sulphur1 by flaming waste and  
vanish into burning ,smoke1 which       
,smoke1 if the ,flame be put out1 is    
very thick and visible1 and sometimes   
smells strongly1 but in the ,flame loses
 its smell by burning1 and according to 
the nature of the ,smoke the ,flame is  
of several ,colours1 as that of ,sulphur
 blue1 that of ,copper open'd with      
sublimate green1 that of ,tallow yellow1
 that of ,camphire white4 ,smoke passing
 through ,flame cannot but grow red hot1

 and red hot ,smoke can have no other   
appearance than that of ,flame4 ,when   
,gun-powder takes fire1 it goes away    
into ,flaming ,smoke4 ,for the ,charcoal
 and ,sulphur easily take fire1 and set 
fire to the ,nitre1 and the ,spirit of  
the ,nitre being thereby rarified into  
,vapour1 rushes out with ,explosion much
 after the manner that the ,vapour of   
,water rushes out of an ,a,eolipile2 the
 ,sulphur also being volatile is        
converted into ,vapour1 and augments the
 ,explosion4 ,and the acid ,vapour of   
the ,sulphur 7namely that which distils 
under a ,bell into ,oil of ,sulphur17   
entring violently into the fix'd ,body  
of the ,nitre1 sets loose the ,spirit of
 the ,nitre1 and excites a great        
,fermentation1 whereby the ,heat is     
farther augmented1 and the fix'd ,body  
of the ,nitre is also rarified into     
,fume1 and the ,explosion is thereby    
made more vehement and quick4 ,for if   
,salt of ,tartar be mix'd with          
,gun-powder1 and that ,mixture be warm'd

 till it takes fire1 the ,explosion will
 be more violent and quick than that of 
,gun-powder alone2 which cannot proceed 
from any other cause than the action of 
the ,vapour of the ,gun-powder upon the 
,salt of ,tartar1 whereby that ,salt is 
rarified4 ,the ,explosion of ,gun-powder
 arises therefore from the violent      
action whereby all the ,mixture being   
quickly and vehemently heated1 is       
rarified and converted into ,fume and   
,vapour3 which ,vapour1 by the violence 
of that action1 becoming so hot as to   
shine1 appears in the form of ,flame4   
,qu4 #aa4 ,do not great ,bodies conserve
 their heat the longest1 their parts    
heating one another1 and may not great  
dense and fix'd ,bodies1 when heated    
beyond a certain degree1 emit ,light so 
copiously1 as by the ,emission and      
,re-action of its ,light1 and the       
,reflexions and ,refractions of its     
,rays within its ,pores to grow still   
hotter1 till it comes to a certain      
period of heat1 such as is that of the  

,sun8 ,and are not the ,sun and fix'd   
,stars great ,earths vehemently hot1    
whose heat is conserved by the greatness
 of the ,bodies1 and the mutual ,action 
and ,reaction between them1 and the     
,light which they emit1 and whose parts 
are kept from fuming away1 not only by  
their fixity1 but also by the vast      
weight and density of the ,atmospheres  
incumbent upon them2 and very strongly  
compressing them1 and condensing the    
,vapours and ,exhalations which arise   
from them8 ,for if ,water be made warm  
in any pellucid ,vessel emptied of ,air1
 that ,water in the ,vacuum will bubble 
and boil as vehemently as it would in   
the open ,air in a ,vessel set upon the 
,fire till it conceives a much greater  
heat4 ,for the weight of the incumbent  
,atmosphere keeps down the ,vapours1 and
 hinders the ,water from boiling1 until 
it grow much hotter than is requisite to
 make it boil in vacuo4 ,also a mixture 
of ,tin and ,lead being put upon a red  
hot ,iron in vacuo emits a ,fume and    

,flame1 but the same ,mixture in the    
open ,air1 by reason of the incumbent   
,atmosphere1 does not so much as emit   
any ,fume which can be perceived by     
,sight4 ,in like manner the great weight
 of the ,atmosphere which lies upon the 
,globe of the ,sun may hinder ,bodies   
there from rising up and going away from
 the ,sun in the form of ,vapours and   
,fumes1 unless by means of a far greater
 heat than that which on the ,surface of
 our ,earth would very easily turn them 
into ,vapours and ,fumes4 ,and the same 
great weight may condense those ,vapours
 and ,exhalations as soon as they shall 
at any time begin to ascend from the    
,sun1 and make them presently fall back 
again into him1 and by that action      
increase his ,heat much after the manner
 that in our ,earth the ,air increases  
the ,heat of a culinary ,fire4 ,and the 
same weight may hinder the ,globe of the
 ,sun from being diminish'd1 unless by  
the ,emission of ,light1 and a very     
small quantity of ,vapours and          

,exhalations4  ,qu4 #ab4 ,do not the    
,rays of ,light in falling upon the     
bottom of the ,eye excite ,vibrations in
 the ,tunica ,retina8 ,which            
,vibrations1 being propagated along the 
solid ,fibres of the optick ,nerves into
 the ,brain1 cause the ,sense of seeing4
 ,for because dense ,bodies conserve    
their ,heat a long time1 and the densest
 ,bodies conserve their ,heat the       
longest1 the ,vibrations of their parts 
are of a lasting nature1 and therefore  
may be propagated along solid ,fibres of
 uniform dense ,matter to a great       
distance1 for conveying into the ,brain 
the impressions made upon all the       
,organs of ,sense4 ,for that ,motion    
which can continue long in one and the  
same part of a ,body1 can be propagated 
a long way from one part to another1    
supposing the ,body homogeneal1 so that 
the ,motion may not be reflected1       
refracted1 interrupted or disorder'd by 
any unevenness of the ,body4  ,qu4 #ac4 
,do not several sorts of ,rays make     

,vibrations of several bignesses1 which 
according to their bignesses excite     
,sensations of several ,colours1 much   
after the manner that the ,vibrations of
 the ,air1 according to their several   
bignesses excite ,sensations of several 
,sounds8 ,and particularly do not the   
most refrangible ,rays excite the       
shortest ,vibrations for making a       
,sensation of deep violet1 the least    
refrangible the largest for making a    
,sensation of deep red1 and the several 
intermediate sorts of ,rays1 ,vibrations
 of several intermediate bignesses to   
make ,sensations of the several         
intermediate ,colours8  ,qu4 #ad4 ,may  
not the harmony and discord of ,colours 
arise from the proportions of the       
,vibrations propagated through the      
,fibres of the optick ,nerves into the  
,brain1 as the harmony and discord of   
,sounds arise from the proportions of   
the ,vibrations of the ,air8 ,for some  
,colours1 if they be view'd together1   
are agreeable to one another1 as those  

of ,gold and ,indigo1 and others        
disagree4  ,qu4 #ae4 ,are not the       
,species of ,objects seen with both     
,eyes united where the optick ,nerves   
meet before they come into the ,brain1  
the ,fibres on the right side of both   
,nerves uniting there1 and after union  
going thence into the ,brain in the     
,nerve which is on the right side of the
 ,head1 and the ,fibres on the left side
 of both ,nerves uniting in the same    
place1 and after union going into the   
,brain in the ,nerve which is on the    
left side of the ,head1 and these two   
,nerves meeting in the ,brain in such a 
manner that their ,fibres make but one  
entire ,species or ,picture1 half of    
which on the right side of the          
,sensorium comes from the right side of 
both ,eyes through the right side of    
both optick ,nerves to the place where  
the ,nerves meet1 and from thence on the
 right side of the ,head into the       
,brain1 and the other half on the left  
side of the ,sensorium comes in like    

manner from the left side of both ,eyes4
 ,for the optick ,nerves of such        
,animals as look the same way with both 
,eyes 7as of ,men1 ,dogs1 ,sheep1 ,oxen1
 c47 meet before they come into the     
,brain1 but the optick ,nerves of such  
,animals as do not look the same way    
with both ,eyes 7as of ,fishes1 and of  
the ,chameleon17 do not meet1 if ,i am  
rightly inform'd4  ,qu4 #af4 ,when a    
,man in the dark presses either corner  
of his ,eye with his ,finger1 and turns 
his ,eye away from his ,finger1 he will 
see a ,circle of ,colours like those in 
the ,feather of a ,peacock's ,tail4 ,if 
the ,eye and the ,finger remain quiet   
these ,colours vanish in a second       
,minute of ,time1 but if the ,finger be 
moved with a quavering ,motion they     
appear again4 ,do not these ,colours    
arise from such ,motions excited in the 
bottom of the ,eye by the ,pressure and 
,motion of the ,finger1 as1 at other    
times are excited there by ,light for   
causing ,vision8 ,and do not the        

,motions once excited continue about a  
,second of ,time before they cease8 ,and
 when a ,man by a stroke upon his ,eye  
sees a flash of ,light1 are not the like
 ,motions excited in the ,retina by the 
stroke8 ,and when a ,coal of ,fire moved
 nimbly in the circumference of a       
,circle1 makes the whole circumference  
appear like a ,circle of ,fire2 is it   
not because the ,motions excited in the 
bottom of the ,eye by the ,rays of      
,light are of a lasting nature1 and     
continue till the ,coal of ,fire in     
going round returns to its former place8
 ,and considering the lastingness of the
 ,motions excited in the bottom of the  
,eye by ,light1 are they not of a       
vibrating nature8  ,qu4 #ag4 ,if a stone
 be thrown into stagnating ,water1 the  
,waves excited thereby continue some    
time to arise in the place where the    
,stone fell into the ,water1 and are    
propagated from thence in concentrick   
,circles upon the ,surface of the ,water
 to great distances4 ,and the           

,vibrations or ,tremors excited in the  
,air by percussion1 continue a little   
time to move from the place of          
percussion in concentrick ,spheres to   
great distances4 ,and in like manner1   
when a ,ray of ,light falls upon the    
,surface of any pellucid ,body1 and is  
there refracted or reflected1 may not   
,waves of ,vibrations1 or ,tremors1 be  
thereby excited in the refracting or    
reflecting ,medium at the point of      
,incidence1 and continue to arise there1
 and to be propagated from thence as    
long as they continue to arise and be   
propagated1 when they are excited in the
 bottom of the ,eye by the ,pressure or 
,motion of the ,finger1 or by the ,light
 which comes from the ,coal of ,fire in 
the ,experiments above-mention'd8 and   
are not these ,vibrations propagated    
from the point of ,incidence to great   
distances8 ,and do they not overtake the
 ,rays of ,light1 and by overtaking them
 successively1 do they not put them into
 the ,fits of easy ,reflexion and easy  

,transmission described above8 ,for if  
the ,rays endeavour to recede from the  
densest part of the ,vibration1 they may
 be alternately accelerated and retarded
 by the ,vibrations overtaking them4    
,qu4 #ah4 ,if in two large tall         
cylindrical ,vessels of ,glass inverted1
 two little ,thermometers be suspended  
so as not to touch the ,vessels1 and the
 ,air be drawn out of one of these      
,vessels1 and these ,vessels thus       
prepared be carried out of a cold place 
into a warm one2 the ,thermometer in    
vacuo will grow warm as much1 and almost
 as soon as the ,thermometer which is   
not in vacuo4 ,and when the ,vessels are
 carried back into the cold place1 the  
,thermometer in vacuo will grow cold    
almost as soon as the other             
,thermometer4 ,is not the ,heat of the  
warm ,room convey'd through the ,vacuum 
by the ,vibrations of a much subtiler   
,medium than ,air1 which after the ,air 
was drawn out remained in the ,vacuum8  
,and is not this ,medium the same with  

that ,medium by which ,light is         
refracted and reflected1 and by whose   
,vibrations ,light communicates ,heat to
 ,bodies1 and is put into ,fits of easy 
,reflexion and easy ,transmission8 ,and 
do not the ,vibrations of this ,medium  
in hot ,bodies contribute to the        
intenseness and duration of their ,heat8
 ,and do not hot ,bodies communicate    
their ,heat to contiguous cold ones1 by 
the ,vibrations of this ,medium         
propagated from them into the cold ones8
 ,and is not this ,medium exceedingly   
more rare and subtile than the ,air1 and
 exceedingly more elastick and active8  
,and doth it not readily pervade all    
,bodies8 ,and is it not 7by its elastick
 force7 expanded through all the        
,heavens8  ,qu4 #ai4 ,doth not the      
,refraction of ,light proceed from the  
different density of this ,a,ethereal   
,medium in different places1 the ,light 
receding always from the denser parts of
 the ,medium8 ,and is not the density   
thereof greater in free and open ,spaces

 void of ,air and other grosser ,bodies1
 than within the ,pores of ,water1      
,glass1 ,crystal1 ,gems1 and other      
compact ,bodies8 ,for when ,light passes
 through ,glass or ,crystal1 and falling
 very obliquely upon the farther        
,surface thereof is totally reflected1  
the total ,reflexion ought to proceed   
rather from the density and vigour of   
the ,medium without and beyond the      
,glass1 than from the rarity and        
weakness thereof4  ,qu4 #bj4 ,doth not  
this ,a,ethereal ,medium in passing out 
of ,water1 ,glass1 ,crystal1 and other  
compact and dense ,bodies into empty    
,spaces1 grow denser and denser by      
degrees1 and by that means refract the  
,rays of ,light not in a point1 but by  
bending them gradually in curve ,lines8 
,and doth not the gradual condensation  
of this ,medium extend to some distance 
from the ,bodies1 and thereby cause the 
,inflexions of the ,rays of ,light1     
which pass by the edges of dense        
,bodies1 at some distance from the      

,bodies8  ,qu4 #ba4 ,is not this ,medium
 much rarer within the dense ,bodies of 
the ,sun1 ,stars1 ,planets and ,comets1 
than in the empty celestial ,spaces     
between them8 ,and in passing from them 
to great distances1 doth it not grow    
denser and denser perpetually1 and      
thereby cause the gravity of those great
 ,bodies towards one another1 and of    
their parts towards the ,bodies2 every  
,body endeavouring to go from the denser
 parts of the ,medium towards the rarer8
 ,for if this ,medium be rarer within   
the ,sun's ,body than at its ,surface1  
and rarer there than at the hundredth   
part of an ,inch from its ,body1 and    
rarer there than at the fiftieth part of
 an ,inch from its ,body1 and rarer     
there than at the ,orb of ,saturn2 ,i   
see no reason why the ,increase of      
density should stop any where1 and not  
rather be continued through all         
distances from the ,sun to ,saturn1 and 
beyond4 ,and though this ,increase of   
density may at great distances be       

exceeding slow1 yet if the elastick     
force of this ,medium be exceeding      
great1 it may suffice to impel ,bodies  
from the denser parts of the ,medium    
towards the rarer1 with all that power  
which we call ,gravity4 ,and that the   
elastick force of this ,medium is       
exceeding great1 may be gather'd from   
the swiftness of its ,vibrations4       
,sounds move about #aadj ,english ,feet 
in a second ,minute of ,time1 and in    
seven or eight ,minutes of ,time they   
move about one hundred ,english ,miles4 
,light moves from the ,sun to us in     
about seven or eight ,minutes of ,time1 
which distance is about #gj1jjj1jjj     
,english ,miles1 supposing the          
horizontal ,parallax of the ,sun to be  
about #ab''4 ,and the ,vibrations or    
,pulses of this ,medium1 that they may  
cause the alternate ,fits of easy       
,transmission and easy ,reflexion1 must 
be swifter than ,light1 and by          
consequence above #gjj1jjj times swifter
 than ,sounds4 ,and therefore the       

elastick force of this ,medium1 in      
proportion to its density1 must be above
 #gjjjjj x #gjjjjj 7that is1 above      
#dij1jjj1jjj1jjj7 times greater than the
 elastick force of the ,air is in       
proportion to its density4 ,for the     
,velocities of the ,pulses of elastick  
,mediums are in a subduplicate ,ratio of
 the ,elasticities and the ,rarities of 
the ,mediums taken together4  ,as       
,attraction is stronger in small        
,magnets than in great ones in          
proportion to their ,bulk1 and ,gravity 
is greater in the ,surfaces of small    
,planets than in those of great ones in 
proportion to their bulk1 and small     
,bodies are agitated much more by       
electric attraction than great ones2 so 
the smallness of the ,rays of ,light may
 contribute very much to the power of   
the ,agent by which they are refracted4 
,and so if any one should suppose that  
,a,ether 7like our ,air7 may contain    
,particles which endeavour to recede    
from one another 7for ,i do not know    

what this ,a,ether is7 and that its     
,particles are exceedingly smaller than 
those of ,air1 or even than those of    
,light3 ,the exceeding smallness of its 
,particles may contribute to the        
greatness of the force by which those   
,particles may recede from one another1 
and thereby make that ,medium           
exceedingly more rare and elastick than 
,air1 and by consequence exceedingly    
less able to resist the motions of      
,projectiles1 and exceedingly more able 
to press upon gross ,bodies1 by         
endeavouring to expand it self4  ,qu4   
#bb4 ,may not ,planets and ,comets1 and 
all gross ,bodies1 perform their        
,motions more freely1 and with less     
resistance in this ,a,ethereal ,medium  
than in any ,fluid1 which fills all     
,space adequately without leaving any   
,pores1 and by consequence is much      
denser than ,quick-silver or ,gold8 ,and
 may not its resistance be so small1 as 
to be inconsiderable8 ,for instance2 ,if
 this ,a,ether 7for so ,i will call it7 

should be supposed #gjjjjj times more   
elastick than our ,air1 and above       
#gjjjjj times more rare2 its resistance 
would be above #fjj1jjj1jjj times less  
than that of ,water4 ,and so small a    
resistance would scarce make any        
sensible alteration in the ,motions of  
the ,planets in ten thousand ,years4 ,if
 any one would ask how a ,medium can be 
so rare1 let him tell me how the ,air1  
in the upper parts of the ,atmosphere1  
can be above an hundred thousand        
thousand times rarer than ,gold4 ,let   
him also tell me1 how an electrick ,body
 can by ,friction emit an ,exhalation so
 rare and subtile1 and yet so potent1 as
 by its ,emission to cause no sensible  
,diminution of the weight of the        
electrick ,body1 and to be expanded     
through a ,sphere1 whose ,diameter is   
above two ,feet1 and yet to be able to  
agitate and carry up ,leaf ,copper1 or  
,leaf ,gold1 at the distance of above a 
,foot from the electrick ,body8 ,and how
 the ,effluvia of a ,magnet can be so   

rare and subtile1 as to pass through a  
,plate of ,glass without any ,resistance
 or ,diminution of their ,force1 and yet
 so potent as to turn a magnetick       
,needle beyond the ,glass8  ,qu4 #bc4   
,is not ,vision perform'd chiefly by the
 ,vibrations of this ,medium1 excited in
 the bottom of the ,eye by the ,rays of 
,light1 and propagated through the      
solid1 pellucid and uniform             
,capillamenta of the optick ,nerves into
 the place of ,sensation8 ,and is not   
,hearing perform'd by the ,vibrations   
either of this or some other ,medium1   
excited in the auditory ,nerves by the  
,tremors of the ,air1 and propagated    
through the solid1 pellucid and uniform 
,capillamenta of those ,nerves into the 
place of ,sensation8 ,and so of the     
other ,senses4  ,qu4 #bd4 ,is not       
,animal ,motion perform'd by the        
,vibrations of this ,medium1 excited in 
the ,brain by the power of the ,will1   
and propagated from thence through the  
solid1 pellucid and uniform             

,capillamenta of the ,nerves into the   
,muscles1 for contracting and dilating  
them8 ,i suppose that the ,capillamenta 
of the ,nerves are each of them solid   
and uniform1 that the vibrating ,motion 
of the ,a,ethereal ,medium may be       
propagated along them from one end to   
the other uniformly1 and without        
interruption3 ,for ,obstructions in the 
,nerves create ,palsies4 ,and that they 
may be sufficiently uniform1 ,i suppose 
them to be pellucid when view'd singly1 
tho' the ,reflexions in their           
cylindrical ,surfaces may make the whole
 ,nerve 7composed of many ,capillamenta7
 appear opake and white4 ,for opacity   
arises from reflecting ,surfaces1 such  
as may disturb and interrupt the        
,motions of this ,medium4  ,sidenote3   
,see the following ,scheme1 p4 #cef4    
,qu4 #be4 ,are there not other original 
,properties of the ,rays of ,light1     
besides those already described8 ,an    
instance of another original ,property  
we have in the ,refraction of ,island   

,crystal1 described first by ,erasmus   
,bartholine1 and afterwards more exactly
 by ,hugenius1 in his ,book ,de la      
,lumiere4 ,this ,crystal is a pellucid  
fissile ,stone1 clear as ,water or      
,crystal of the ,rock1 and without      
,colour2 enduring a red ,heat without   
losing its transparency1 and in a very  
strong ,heat calcining without ,fusion4 
,steep'd a ,day or two in ,water1 it    
loses its natural ,polish4 ,being rubb'd
 on ,cloth1 it attracts pieces of       
,straws and other light things1 like    
,ambar or ,glass2 and with ,aqua fortis 
it makes an ,ebullition4 ,it seems to be
 a sort of ,talk1 and is found in form  
of an oblique ,parallelopiped1 with six 
parallelogram ,sides and eight solid    
,angles4 ,the obtuse ,angles of the     
,parallelograms are each of them #aja   
,degrees and #eb ,minutes2 the acute    
ones #gh ,degrees and #h ,minutes4 ,two 
of the solid ,angles opposite to one    
another1 as ,c and ,e1 are compassed    
each of them with three of these obtuse 

,angles1 and each of the other six with 
one obtuse and two acute ones4 ,it      
cleaves easily in planes parallel to any
 of its ,sides1 and not in any other    
,planes4 ,it cleaves with a glossy      
polite ,surface not perfectly plane1 but
 with some little unevenness4 ,it is    
easily scratch'd1 and by reason of its  
softness it takes a ,polish very        
difficultly4 ,it polishes better upon   
polish'd ,looking-glass than upon       
,metal1 and perhaps better upon ,pitch1 
,leather or ,parchment4 ,afterwards it  
must be rubb'd with a little ,oil or    
white of an ,egg1 to fill up its        
,scratches2 whereby it will become very 
transparent and polite4 ,but for several
 ,experiments1 it is not necessary to   
polish it4 ,if a piece of this          
crystalline ,stone be laid upon a ,book1
 every ,letter of the ,book seen through
 it will appear double1 by means of a   
double ,refraction4 ,and if any beam of 
,light falls either perpendicularly1 or 
in any oblique ,angle upon any ,surface 

of this ,crystal1 it becomes divided    
into two beams by means of the same     
double ,refraction4 ,which beams are of 
the same ,colour with the incident beam 
of ,light1 and seem equal to one another
 in the quantity of their ,light1 or    
very nearly equal4 ,one of these        
,refractions is perform'd by the usual  
,rule of ,opticks1 the ,sine of         
,incidence out of ,air into this        
,crystal being to the ,sine of          
,refraction1 as five to three4 ,the     
other ,refraction1 which may be called  
the unusual ,refraction1 is perform'd by
 the following ,rule4  ,illustration3   
,,fig4 #d4  ,let ,,adbc represent the   
refracting ,surface of the ,crystal1 ,c 
the biggest solid ,angle at that        
,surface1 ,,gehf the opposite ,surface1 
and ,,ck a perpendicular on that        
,surface4 ,this perpendicular makes with
 the edge of the ,crystal ,,cf1 an      
,angle of #ai ,degr4 #c'4 ,join ,,kf1   
and in it take ,,kl1 so that the ,angle 
,,kcl be #f ,degr4 #dj'4 and the ,angle 

,,lcf #ab ,degr4 #bc'4 ,and if ,,st     
represent any beam of ,light incident at
 ,t in any ,angle upon the refracting   
,surface ,,adbc1 let ,,tv be the        
refracted beam determin'd by the given  
,portion of the ,sines #e to #c1        
according to the usual ,rule of         
,opticks4 ,draw ,,vx parallel and equal 
to ,,kl4 ,draw it the same way from ,v  
in which ,l lieth from ,k2 and joining  
,,tx1 this line ,,tx shall be the other 
refracted beam carried from ,t to ,x1 by
 the unusual ,refraction4  ,if therefore
 the incident beam ,,st be perpendicular
 to the refracting ,surface1 the two    
beams ,,tv and ,,tx1 into which it shall
 become divided1 shall be parallel to   
the lines ,,ck and ,,cl2 one of those   
beams going through the ,crystal        
perpendicularly1 as it ought to do by   
the usual ,laws of ,opticks1 and the    
other ,,tx by an unusual ,refraction    
diverging from the perpendicular1 and   
making with it an ,angle ,,vtx of about 
#f-b_/c ,degrees1 as is found by        

,experience4 ,and hence1 the ,plane     
,,vtx1 and such like ,planes which are  
parallel to the ,plane ,,cfk1 may be    
called the ,planes of perpendicular     
,refraction4 ,and the ,coast towards    
which the lines ,,kl and ,,vx are drawn1
 may be call'd the ,coast of unusual    
,refraction4  ,in like manner ,crystal  
of the ,rock has a double ,refraction3  
,but the difference of the two          
,refractions is not so great and        
manifest as in ,island ,crystal4  ,when 
the beam ,,st incident on ,island       
,crystal is divided into two beams ,,tv 
and ,,tx1 and these two beams arrive at 
the farther ,surface of the ,glass2 the 
beam ,,tv1 which was refracted at the   
first ,surface after the usual manner1  
shall be again refracted entirely after 
the usual manner at the second ,surface2
 and the beam ,,tx1 which was refracted 
after the unusual manner in the first   
,surface1 shall be again refracted      
entirely after the unusual manner in the
 second ,surface2 so that both these    

beams shall emerge out of the second    
,surface in lines parallel to the first 
incident beam ,,st4  ,and if two pieces 
of ,island ,crystal be placed one after 
another1 in such manner that all the    
,surfaces of the latter be parallel to  
all the corresponding ,surfaces of the  
former3 ,the ,rays which are refracted  
after the usual manner in the first     
,surface of the first ,crystal1 shall be
 refracted after the usual manner in all
 the following ,surfaces2 and the ,rays 
which are refracted after the unusual   
manner in the first ,surface1 shall be  
refracted after the unusual manner in   
all the following ,surfaces4 ,and the   
same thing happens1 though the ,surfaces
 of the ,crystals be any ways inclined  
to one another1 provided that their     
,planes of perpendicular ,refraction be 
parallel to one another4  ,and therefore
 there is an original difference in the 
,rays of ,light1 by means of which some 
,rays are in this ,experiment constantly
 refracted after the usual manner1 and  

others constantly after the unusual     
manner3 ,for if the difference be not   
original1 but arises from new           
,modifications impress'd on the ,rays at
 their first ,refraction1 it would be   
alter'd by new ,modifications in the    
three following ,refractions2 whereas it
 suffers no alteration1 but is constant1
 and has the same effect upon the ,rays 
in all the ,refractions4 ,the unusual   
,refraction is therefore perform'd by an
 original property of the ,rays4 ,and it
 remains to be enquired1 whether the    
,rays have not more original ,properties
 than are yet discover'd4  ,qu4 #bf4    
,have not the ,rays of ,light several   
sides1 endued with several original     
,properties8 ,for if the ,planes of     
perpendicular ,refraction of the second 
,crystal be at right ,angles with the   
,planes of perpendicular ,refraction of 
the first ,crystal1 the ,rays which are 
refracted after the usual manner in     
passing through the first ,crystal1 will
 be all of them refracted after the     

unusual manner in passing through the   
second ,crystal2 and the ,rays which are
 refracted after the unusual manner in  
passing through the first ,crystal1 will
 be all of them refracted after the     
usual manner in passing through the     
second ,crystal4 ,and therefore there   
are not two sorts of ,rays differing in 
their nature from one another1 one of   
which is constantly and in all          
,positions refracted after the usual    
manner1 and the other constantly and in 
all ,positions after the unusual manner4
 ,the difference between the two sorts  
of ,rays in the ,experiment mention'd in
 the #beth ,question1 was only in the   
,positions of the ,sides of the ,rays to
 the ,planes of perpendicular           
,refraction4 ,for one and the same ,ray 
is here refracted sometimes after the   
usual1 and sometimes after the unusual  
manner1 according to the ,position which
 its ,sides have to the ,crystals4 ,if  
the ,sides of the ,ray are posited the  
same way to both ,crystals1 it is       

refracted after the same manner in them 
both3 ,but if that side of the ,ray     
which looks towards the ,coast of the   
unusual ,refraction of the first        
,crystal1 be #ij ,degrees from that side
 of the same ,ray which looks toward the
 ,coast of the unusual ,refraction of   
the second ,crystal1 7which may be      
effected by varying the ,position of the
 second ,crystal to the first1 and by   
consequence to the ,rays of ,light17 the
 ,ray shall be refracted after several  
manners in the several ,crystals4 ,there
 is nothing more required to determine  
whether the ,rays of ,light which fall  
upon the second ,crystal shall be       
refracted after the usual or after the  
unusual manner1 but to turn about this  
,crystal1 so that the ,coast of this    
,crystal's unusual ,refraction may be on
 this or on that side of the ,ray4 ,and 
therefore every ,ray may be consider'd  
as having four ,sides or ,quarters1 two 
of which opposite to one another incline
 the ,ray to be refracted after the     

unusual manner1 as often as either of   
them are turn'd towards the ,coast of   
unusual ,refraction2 and the other two1 
whenever either of them are turn'd      
towards the ,coast of unusual           
,refraction1 do not incline it to be    
otherwise refracted than after the usual
 manner4 ,the two first may therefore be
 call'd the ,sides of unusual           
,refraction4 ,and since these           
,dispositions were in the ,rays before  
their ,incidence on the second1 third1  
and fourth ,surfaces of the two         
,crystals1 and suffered no alteration   
7so far as appears17 by the ,refraction 
of the ,rays in their passage through   
those ,surfaces1 and the ,rays were     
refracted by the same ,laws in all the  
four ,surfaces2 it appears that those   
,dispositions were in the ,rays         
originally1 and suffer'd no alteration  
by the first ,refraction1 and that by   
means of those ,dispositions the ,rays  
were refracted at their ,incidence on   
the first ,surface of the first         

,crystal1 some of them after the usual1 
and some of them after the unusual      
manner1 accordingly as their ,sides of  
unusual ,refraction were then turn'd    
towards the ,coast of the unusual       
,refraction of that ,crystal1 or        
sideways from it4  ,every ,ray of ,light
 has therefore two opposite ,sides1     
originally endued with a ,property on   
which the unusual ,refraction depends1  
and the other two opposite ,sides not   
endued with that ,property4 ,and it     
remains to be enquired1 whether there   
are not more ,properties of ,light by   
which the ,sides of the ,rays differ1   
and are distinguished from one another4 
,in explaining the difference of the    
,sides of the ,rays above mention'd1 ,i 
have supposed that the ,rays fall       
perpendicularly on the first ,crystal4  
,but if they fall obliquely on it1 the  
,success is the same4 ,those ,rays which
 are refracted after the usual manner in
 the first ,crystal1 will be refracted  
after the unusual manner in the second  

,crystal1 supposing the ,planes of      
perpendicular ,refraction to be at right
 ,angles with one another1 as above2 and
 on the contrary4  ,if the ,planes of   
the perpendicular ,refraction of the two
 ,crystals be neither parallel nor      
perpendicular to one another1 but       
contain an acute ,angle3 ,the two beams 
of ,light which emerge out of the first 
,crystal1 will be each of them divided  
into two more at their ,incidence on the
 second ,crystal4 ,for in this case the 
,rays in each of the two beams will some
 of them have their ,sides of unusual   
,refraction1 and some of them their     
other ,sides turn'd towards the ,coast  
of the unusual ,refraction of the second
 ,crystal4  ,qu4 #bg4 ,are not all      
,hypotheses erroneous which have        
hitherto been invented for explaining   
the ,phaenomena of ,light1 by new       
,modifications of the ,rays8 ,for those 
,phaenomena depend not upon new         
,modifications1 as has been supposed1   
but upon the original and unchangeable  

,properties of the ,rays4  ,qu4 #bh4    
,are not all ,hypotheses erroneous1 in  
which ,light is supposed to consist in  
,pression or ,motion1 propagated through
 a fluid ,medium8 ,for in all these     
,hypotheses the ,phaenomena of ,light   
have been hitherto explain'd by         
supposing that they arise from new      
,modifications of the ,rays2 which is an
 erroneous ,supposition4  ,if ,light    
consisted only in ,pression propagated  
without actual ,motion1 it would not be 
able to agitate and heat the ,bodies    
which refract and reflect it4 ,if it    
consisted in ,motion propagated to all  
distances in an instant1 it would       
require an infinite force every moment1 
in every shining ,particle1 to generate 
that ,motion4 ,and if it consisted in   
,pression or ,motion1 propagated either 
in an instant or in time1 it would bend 
into the ,shadow4 ,for ,pression or     
,motion cannot be propagated in a ,fluid
 in right ,lines1 beyond an ,obstacle   
which stops part of the ,motion1 but    

will bend and spread every way into the 
quiescent ,medium which lies beyond the 
,obstacle4 ,gravity tends downwards1 but
 the ,pressure of ,water arising from   
,gravity tends every way with equal     
,force1 and is propagated as readily1   
and with as much force sideways as      
downwards1 and through crooked passages 
as through strait ones4 ,the ,waves on  
the ,surface of stagnating ,water1      
passing by the sides of a broad         
,obstacle which stops part of them1 bend
 afterwards and dilate themselves       
gradually into the quiet ,water behind  
the ,obstacle4 ,the ,waves1 ,pulses or  
,vibrations of the ,air1 wherein ,sounds
 consist1 bend manifestly1 though not so
 much as the ,waves of ,water4 ,for a   
,bell or a ,cannon may be heard beyond a
 ,hill which intercepts the sight of the
 sounding ,body1 and ,sounds are        
propagated as readily through crooked   
,pipes as through streight ones4 ,but   
,light is never known to follow crooked 
,passages nor to bend into the ,shadow4 

,for the fix'd ,stars by the            
,interposition of any of the ,planets   
cease to be seen4 ,and so do the ,parts 
of the ,sun by the ,interposition of the
 ,moon1 ,mercury or ,venus4 ,the ,rays  
which pass very near to the edges of any
 ,body1 are bent a little by the action 
of the ,body1 as we shew'd above2 but   
this bending is not towards but from the
 ,shadow1 and is perform'd only in the  
passage of the ,ray by the ,body1 and at
 a very small distance from it4 ,so soon
 as the ,ray is past the ,body1 it goes 
right on4  ,sidenote3 ,mais pour dire   
comment cela se fait1 je n'ay rien trove
 jusqu' ici qui me satisfasse4 ,c4 ,h4  
de la lumiere1 c4 #e1 p4 #ia4  ,to      
explain the unusual ,refraction of      
,island ,crystal by ,pression or ,motion
 propagated1 has not hitherto been      
attempted 7to my knowledge7 except by   
,huygens1 who for that end supposed two 
several vibrating ,mediums within that  
,crystal4 ,but when he tried the        
,refractions in two successive pieces of

 that ,crystal1 and found them such as  
is mention'd above2 he confessed himself
 at a loss for explaining them4 ,for    
,pressions or ,motions1 propagated from 
a shining ,body through an uniform      
,medium1 must be on all sides alike2    
whereas by those ,experiments it        
appears1 that the ,rays of ,light have  
different ,properties in their different
 ,sides4 ,he suspected that the ,pulses 
of ,a,ether in passing through the first
 ,crystal might receive certain new     
,modifications1 which might determine   
them to be propagated in this or that   
,medium within the second ,crystal1     
according to the ,position of that      
,crystal4 ,but what ,modifications those
 might be he could not say1 nor think of
 any thing satisfactory in that ,point4 
,and if he had known that the unusual   
,refraction depends not on new          
,modifications1 but on the original and 
unchangeable ,dispositions of the ,rays1
 he would have found it as difficult to 
explain how those ,dispositions which he

 supposed to be impress'd on the ,rays  
by the first ,crystal1 could be in them 
before their ,incidence on that         
,crystal1 and in general1 how all ,rays 
emitted by shining ,bodies1 can have    
those ,dispositions in them from the    
beginning4 ,to me1 at least1 this seems 
inexplicable1 if ,light be nothing else 
than ,pression or ,motion propagated    
through ,a,ether4  ,and it is as        
difficult to explain by these           
,hypotheses1 how ,rays can be           
alternately in ,fits of easy ,reflexion 
and easy ,transmission2 unless perhaps  
one might suppose that there are in all 
,space two ,a,ethereal vibrating        
,mediums1 and that the ,vibrations of   
one of them constitute ,light1 and the  
,vibrations of the other are swifter1   
and as often as they overtake the       
,vibrations of the first1 put them into 
those ,fits4 ,but how two ,a,ethers can 
be diffused through all ,space1 one of  
which acts upon the other1 and by       
consequence is re-acted upon1 without   

retarding1 shattering1 dispersing and   
confounding one anothers ,motions1 is   
inconceivable4 ,and against filling the 
,heavens with fluid ,mediums1 unless    
they be exceeding rare1 a great         
,objection arises from the regular and  
very lasting ,motions of the ,planets   
and ,comets in all manner of ,courses   
through the ,heavens4 ,for thence it is 
manifest1 that the ,heavens are void of 
all sensible ,resistance1 and by        
consequence of all sensible ,matter4    
,for the resisting ,power of fluid      
,mediums arises partly from the         
,attrition of the ,parts of the ,medium1
 and partly from the ,vis inertiae of   
the ,matter4 ,that part of the          
,resistance of a spherical ,body which  
arises from the ,attrition of the ,parts
 of the ,medium is very nearly as the   
,diameter1 or1 at the most1 as the      
,factum of the ,diameter1 and the       
,velocity of the spherical ,body        
together4 ,and that part of the         
,resistance which arises from the ,vis  

inertiae of the ,matter1 is as the      
,square of that ,factum4 ,and by this   
difference the two sorts of ,resistance 
may be distinguish'd from one another in
 any ,medium2 and these being           
distinguish'd1 it will be found that    
almost all the ,resistance of ,bodies of
 a competent ,magnitude moving in ,air1 
,water1 ,quick-silver1 and such like    
,fluids with a competent ,velocity1     
arises from the ,vis inertiae of the    
,parts of the ,fluid4  ,now that part of
 the resisting ,power of any ,medium    
which arises from the ,tenacity1        
,friction or ,attrition of the ,parts of
 the ,medium1 may be diminish'd by      
dividing the ,matter into smaller       
,parts1 and making the ,parts more      
smooth and slippery3 ,but that part of  
the ,resistance which arises from the   
,vis inertiae1 is proportional to the   
,density of the ,matter1 and cannot be  
diminish'd by dividing the ,matter into 
smaller ,parts1 nor by any other means  
than by decreasing the ,density of the  

,medium4 ,and for these ,reasons the    
,density of fluid ,mediums is very      
nearly proportional to their            
,resistance4 ,liquors which differ not  
much in ,density1 as ,water1 ,spirit of 
,wine1 ,spirit of ,turpentine1 hot ,oil1
 differ not much in ,resistance4 ,water 
is thirteen or fourteen times lighter   
than ,quick-silver and by consequence   
thirteen or fourteen times rarer1 and   
its ,resistance is less than that of    
,quick-silver in the same ,proportion1  
or thereabouts1 as ,i have found by     
,experiments made with ,pendulums4 ,the 
open ,air in which we breathe is eight  
or nine hundred times lighter than      
,water1 and by consequence eight or nine
 hundred times rarer1 and accordingly   
its ,resistance is less than that of    
,water in the same ,proportion1 or      
thereabouts2 as ,i have also found by   
,experiments made with ,pendulums4 ,and 
in thinner ,air the ,resistance is still
 less1 and at length1 by ratifying the  
,air1 becomes insensible4 ,for small    

,feathers falling in the open ,air meet 
with great ,resistance1 but in a tall   
,glass well emptied of ,air1 they fall  
as fast as ,lead or ,gold1 as ,i have   
seen tried several times4 ,whence the   
,resistance seems still to decrease in  
proportion to the ,density of the       
,fluid4 ,for ,i do not find by any      
,experiments1 that ,bodies moving in    
,quick-silver1 ,water or ,air1 meet with
 any other sensible ,resistance than    
what arises from the ,density and       
,tenacity of those sensible ,fluids1 as 
they would do if the ,pores of those    
,fluids1 and all other ,spaces1 were    
filled with a dense and subtile ,fluid4 
,now if the ,resistance in a ,vessel    
well emptied of ,air1 was but an hundred
 times less than in the open ,air1 it   
would be about a million of times less  
than in ,quick-silver4 ,but it seems to 
be much less in such a ,vessel1 and     
still much less in the ,heavens1 at the 
height of three or four hundred ,miles  
from the ,earth1 or above4 ,for ,mr4    

,boyle has shew'd that ,air may be      
rarified above ten thousand times in    
,vessels of ,glass2 and the ,heavens are
 much emptier of ,air than any ,vacuum  
we can make below4 ,for since the ,air  
is compress'd by the ,weight of the     
incumbent ,atmosphere1 and the ,density 
of ,air is proportional to the ,force   
compressing it1 it follows by           
,computation1 that at the height of     
about seven and a half ,english ,miles  
from the ,earth1 the ,air is four times 
rarer than at the ,surface of the       
,earth2 and at the height of #ae ,miles 
it is sixteen times rarer than that at  
the ,surface of the ,earth2 and at the  
height of #bb-a_/b1 #cj1 or #ch ,miles1 
it is respectively #fd1 #bef1 or #ajbd  
times rarer1 or thereabouts2 and at the 
height of #gf1 #aeb1 #bbh ,miles1 it is 
about #ajjjjjj1 #ajjjjjjjjjjjj1 or      
#ajjjjjjjjjjjjjjjjjj times rarer2 and so
 on4  ,heat promotes ,fluidity very much
 by diminishing the ,tenacity of        
,bodies4 ,it makes many ,bodies fluid   

which are not fluid in cold1 and        
increases the ,fluidity of tenacious    
,liquids1 as of ,oil1 ,balsam1 and      
,honey1 and thereby decreases their     
,resistance4 ,but it decreases not the  
,resistance of ,water considerably1 as  
it would do if any considerable part of 
the ,resistance of ,water arose from the
 ,attrition or ,tenacity of its ,parts4 
,and therefore the ,resistance of ,water
 arises principally and almost entirely 
from the ,vis inertiae of its ,matter2  
and by consequence1 if the ,heavens were
 as dense as ,water1 they would not have
 much less ,resistance than ,water2 if  
as dense as ,quick-silver1 they would   
not have much less ,resistance than     
,quick-silver2 if absolutely dense1 or  
full of ,matter without any ,vacuum1 let
 the ,matter be never so subtil and     
fluid1 they would have a greater        
,resistance than ,quick-silver4 ,a solid
 ,globe in such a ,medium would lose    
above half its ,motion in moving three  
times the length of its ,diameter1 and a

 ,globe not solid 7such as are the      
,planets17 would be retarded sooner4    
,and therefore to make way for the      
regular and lasting ,motions of the     
,planets and ,comets1 it's necessary to 
empty the ,heavens of all ,matter1      
except perhaps some very thin ,vapours1 
,steams1 or ,effluvia1 arising from the 
,atmospheres of the ,earth1 ,planets1   
and ,comets1 and from such an           
exceedingly rare ,a,ethereal ,medium as 
we described above4 ,a dense ,fluid can 
be of no use for explaining the         
,phaenomena of ,nature1 the ,motions of 
the ,planets and ,comets being better   
explain'd without it4 ,it serves only to
 disturb and retard the ,motions of     
those great ,bodies1 and make the ,frame
 of ,nature languish3 ,and in the ,pores
 of ,bodies1 it serves only to stop the 
vibrating ,motions of their ,parts1     
wherein their ,heat and ,activity       
consists4 ,and as it is of no use1 and  
hinders the ,operations of ,nature1 and 
makes her languish1 so there is no      

evidence for its ,existence1 and        
therefore it ought to be rejected4 ,and 
if it be rejected1 the ,hypotheses that 
,light consists in ,pression or ,motion1
 propagated through such a ,medium1 are 
rejected with it4  ,and for rejecting   
such a ,medium1 we have the ,authority  
of those the oldest and most celebrated 
,philosophers of ,greece and ,phoenicia1
 who made a ,vacuum1 and ,atoms1 and the
 ,gravity of ,atoms1 the first          
,principles of their ,philosophy2       
tacitly attributing ,gravity to some    
other ,cause than dense ,matter4 ,later 
,philosophers banish the ,consideration 
of such a ,cause out of natural         
,philosophy1 feigning ,hypotheses for   
explaining all things mechanically1 and 
referring other ,causes to              
,metaphysicks3 ,whereas the main        
,business of natural ,philosophy is to  
argue from ,phaenomena without feigning 
,hypotheses1 and to deduce ,causes from 
,effects1 till we come to the very first
 ,cause1 which certainly is not         

mechanical2 and not only to unfold the  
,mechanism of the ,world1 but chiefly to
 resolve these and such like ,questions4
 ,what is there in places almost empty  
of ,matter1 and whence is it that the   
,sun and ,planets gravitate towards one 
another1 without dense ,matter between  
them8 ,whence is it that ,nature doth   
nothing in vain2 and whence arises all  
that ,order and ,beauty which we see in 
the ,world8 ,to what end are ,comets1   
and whence is it that ,planets move all 
one and the same way in ,orbs           
concentrick1 while ,comets move all     
manner of ways in ,orbs very excentrick2
 and what hinders the fix'd ,stars from 
falling upon one another8 ,how came the 
,bodies of ,animals to be contrived with
 so much ,art1 and for what ends were   
their several ,parts8 ,was the ,eye     
contrived without ,skill in ,opticks1   
and the ,ear without ,knowledge of      
,sounds8 ,how do the ,motions of the    
,body follow from the ,will1 and whence 
is the ,instinct in ,animals8 ,is not   

the ,sensory of ,animals that place to  
which the sensitive ,substance is       
present1 and into which the sensible    
,species of ,things are carried through 
the ,nerves and ,brain1 that there they 
may be perceived by their immediate     
presence to that ,substance8 ,and these 
things being rightly dispatch'd1 does it
 not appear from ,phaenomena that there 
is a ,being incorporeal1 living1        
intelligent1 omnipresent1 who in        
infinite ,space1 as it were in his      
,sensory1 sees the things themselves    
intimately1 and throughly perceives     
them1 and comprehends them wholly by    
their immediate presence to himself3 ,of
 which things the ,images only carried  
through the ,organs of ,sense into our  
little ,sensoriums1 are there seen and  
beheld by that which in us perceives and
 thinks4 ,and though every true ,step   
made in this ,philosophy brings us not  
immediately to the ,knowledge of the    
first ,cause1 yet it brings us nearer to
 it1 and on that account is to be highly

 valued4  ,qu4 #bi4 ,are not the ,rays  
of ,light very small ,bodies emitted    
from shining ,substances8 ,for such     
,bodies will pass through uniform       
,mediums in right ,lines without bending
 into the ,shadow1 which is the ,nature 
of the ,rays of ,light4 ,they will also 
be capable of several ,properties1 and  
be able to conserve their ,properties   
unchanged in passing through several    
,mediums1 which is another ,condition of
 the ,rays of ,light4 ,pellucid         
,substances act upon the ,rays of ,light
 at a distance in refracting1           
reflecting1 and inflecting them1 and the
 ,rays mutually agitate the ,parts of   
those ,substances at a distance for     
heating them2 and this ,action and      
,re-action at a distance very much      
resembles an attractive ,force between  
,bodies4 ,if ,refraction be perform'd by
 ,attraction of the ,rays1 the ,sines of
 ,incidence must be to the ,sines of    
,refraction in a given ,proportion1 as  
we shew'd in our ,principles of         

,philosophy3 ,and this ,rule is true by 
,experience4 ,the ,rays of ,light in    
going out of ,glass into a ,vacuum1 are 
bent towards the ,glass2 and if they    
fall too obliquely on the ,vacuum1 they 
are bent backwards into the ,glass1 and 
totally reflected2 and this ,reflexion  
cannot be ascribed to the ,resistance of
 an absolute ,vacuum1 but must be caused
 by the ,power of the ,glass attracting 
the ,rays at their going out of it into 
the ,vacuum1 and bringing them back4    
,for if the farther ,surface of the     
,glass be moisten'd with ,water or clear
 ,oil1 or liquid and clear ,honey1 the  
,rays which would otherwise be reflected
 will go into the ,water1 ,oil1 or      
,honey2 and therefore are not reflected 
before they arrive at the farther       
,surface of the ,glass1 and begin to go 
out of it4 ,if they go out of it into   
the ,water1 ,oil1 or ,honey1 they go on1
 because the ,attraction of the ,glass  
is almost balanced and rendered         
ineffectual by the contrary ,attraction 

of the ,liquor4 ,but if they go out of  
it into a ,vacuum which has no          
,attraction to balance that of the      
,glass1 the ,attraction of the ,glass   
either bends and refracts them1 or      
brings them back and reflects them4 ,and
 this is still more evident by laying   
together two ,prisms of ,glass1 or two  
,object-glasses of very long            
,telescopes1 the one plane1 the other a 
little convex1 and so compressing them  
that they do not fully touch1 nor are   
too far asunder4 ,for the ,light which  
falls upon the farther ,surface of the  
first ,glass where the ,interval between
 the ,glasses is not above the ten      
hundred thousandth ,part of an ,inch1   
will go through that ,surface1 and      
through the ,air or ,vacuum between the 
,glasses1 and enter into the second     
,glass1 as was explain'd in the first1  
fourth1 and eighth ,observations of the 
first ,part of the second ,book4 ,but1  
if the second ,glass be taken away1 the 
,light which goes out of the second     

,surface of the first ,glass into the   
,air or ,vacuum1 will not go on         
forwards1 but turns back into the first 
,glass1 and is reflected2 and therefore 
it is drawn back by the ,power of the   
first ,glass1 there being nothing else  
to turn it back4 ,nothing more is       
requisite for producing all the variety 
of ,colours1 and degrees of             
,refrangibility1 than that the ,rays of 
,light be ,bodies of different ,sizes1  
the least of which may take violet the  
weakest and darkest of the ,colours1 and
 be more easily diverted by refracting  
,surfaces from the right ,course2 and   
the rest as they are bigger and bigger1 
may make the stronger and more lucid    
,colours1 blue1 green1 yellow1 and red1 
and be more and more difficultly        
diverted4 ,nothing more is requisite for
 putting the ,rays of ,light into ,fits 
of easy ,reflexion and easy             
,transmission1 than that they be small  
,bodies which by their attractive       
,powers1 or some other ,force1 stir up  

,vibrations in what they act upon1 which
 ,vibrations being swifter than the     
,rays1 overtake them successively1 and  
agitate them so as by turns to increase 
and decrease their ,velocities1 and     
thereby put them into those ,fits4 ,and 
lastly1 the unusual ,refraction of      
,island-,crystal looks very much as if  
it were perform'd by some kind of       
attractive virtue lodged in certain     
,sides both of the ,rays1 and of the    
,particles of the ,crystal4 ,for were it
 not for some kind of ,disposition or   
,virtue lodged in some ,sides of the    
,particles of the ,crystal1 and not in  
their other ,sides1 and which inclines  
and bends the ,rays towards the ,coast  
of unusual ,refraction1 the ,rays which 
fall perpendicularly on the ,crystal1   
would not be refracted towards that     
,coast rather than towards any other    
,coast1 both at their ,incidence and at 
their ,emergence1 so as to emerge       
perpendicularly by a contrary ,situation
 of the ,coast of unusual ,refraction at

 the second ,surface2 the ,crystal      
acting upon the ,rays after they have   
pass'd through it1 and are emerging into
 the ,air2 or1 if you please1 into a    
,vacuum4 ,and since the ,crystal by this
 ,disposition or ,virtue does not act   
upon the ,rays1 unless when one of their
 ,sides of unusual ,refraction looks    
towards that ,coast1 this argues a      
,virtue or ,disposition in those ,sides 
of the ,rays1 which answers to1 and     
sympathizes with that ,virtue or        
,disposition of the ,crystal1 as the    
,poles of two ,magnets answer to one    
another4 ,and as ,magnetism may be      
intended and remitted1 and is found only
 in the ,magnet and in ,iron3 ,so this  
,virtue of refracting the perpendicular 
,rays is greater in ,island-,crystal1   
less in ,crystal of the ,rock1 and is   
not yet found in other ,bodies4 ,i do   
not say that this ,virtue is magnetical3
 ,it seems to be of another kind4 ,i    
only say1 that whatever it be1 it's     
difficult to conceive how the ,rays of  

,light1 unless they be ,bodies1 can have
 a permanent ,virtue in two of their    
,sides which is not in their other      
,sides1 and this without any regard to  
their ,position to the ,space or ,medium
 through which they pass4  ,what ,i mean
 in this ,question by a ,vacuum1 and by 
the ,attractions of the ,rays of ,light 
towards ,glass or ,crystal1 may be      
understood by what was said in the      
#ahth1 #aith1 and #bjth ,questions4     
,quest4 #cj4 ,are not gross ,bodies and 
,light convertible into one another1 and
 may not ,bodies receive much of their  
,activity from the ,particles of ,light 
which enter their ,composition8 ,for all
 fix'd ,bodies being heated emit ,light 
so long as they continue sufficiently   
hot1 and ,light mutually stops in       
,bodies as often as its ,rays strike    
upon their ,parts1 as we shew'd above4  
,i know no ,body less apt to shine than 
,water2 and yet ,water by frequent      
,distillations changes into fix'd       
,earth1 as ,mr4 ,boyle has try'd2 and   

then this ,earth being enabled to endure
 a sufficient ,heat1 shines by ,heat    
like other ,bodies4  ,the changing of   
,bodies into ,light1 and ,light into    
,bodies1 is very conformable to the     
,course of ,nature1 which seems         
delighted with ,transmutations4 ,water1 
which is a very fluid tasteless ,salt1  
she changes by ,heat into ,vapour1 which
 is a sort of ,air1 and by ,cold into   
,ice1 which is a hard1 pellucid1        
brittle1 fusible ,stone2 and this ,stone
 returns into ,water by ,heat1 and      
,vapour returns into ,water by ,cold4   
,earth by ,heat becomes ,fire1 and by   
,cold returns into ,earth4 ,dense       
,bodies by ,fermentation rarify into    
several sorts of ,air1 and this ,air by 
,fermentation1 and sometimes without it1
 returns into dense ,bodies4 ,mercury   
appears sometimes in the form of a fluid
 ,metal1 sometimes in the form of a hard
 brittle ,metal1 sometimes in the form  
of a corrosive pellucid ,salt call'd    
,sublimate1 sometimes in the form of a  

tasteless1 pellucid1 volatile white     
,earth1 call'd ,mercurius ,dulcis2 or in
 that of a red opake volatile ,earth1   
call'd ,cinnaber2 or in that of a red or
 white ,precipitate1 or in that of a    
fluid ,salt2 and in ,distillation it    
turns into ,vapour1 and being agitated  
in ,vacuo1 it shines like ,fire4 ,and   
after all these ,changes it returns     
again into its first form of ,mercury4  
,eggs grow from insensible ,magnitudes1 
and change into ,animals2 ,tadpoles into
 ,frogs2 and ,worms into ,flies4 ,all   
,birds1 ,beasts and ,fishes1 ,insects1  
,trees1 and other ,vegetables1 with     
their several ,parts1 grow out of ,water
 and watry ,tinctures and ,salts1 and by
 ,putrefaction return again into watry  
,substances4 ,and ,water standing a few 
,days in the open ,air1 yields a        
,tincture1 which 7like that of ,malt7 by
 standing longer yields a ,sediment and 
a ,spirit1 but before ,putrefaction is  
fit ,nourishment for ,animals and       
,vegetables4 ,and among such various and

 strange ,transmutations1 why may not   
,nature change ,bodies into ,light1 and 
,light into ,bodies8  ,quest4 #ca4 ,have
 not the small ,particles of ,bodies    
certain ,powers1 ,virtues1 or ,forces1  
by which they act at a distance1 not    
only upon the ,rays of ,light for       
reflecting1 refracting1 and inflecting  
them1 but also upon one another for     
producing a great ,part of the          
,phaenomena of ,nature8 ,for it's well  
known1 that ,bodies act one upon another
 by the ,attractions of ,gravity1       
,magnetism1 and ,electricity2 and these 
,instances shew the ,tenor and ,course  
of ,nature1 and make it not improbable  
but that there may be more attractive   
,powers than these4 ,for ,nature is very
 consonant and conformable to her self4 
,how these ,attractions may be          
perform'd1 ,i do not here consider4     
,what ,i call ,attraction may be        
perform'd by impulse1 or by some other  
means unknown to me4 ,i use that ,word  
here to signify only in general any     

,force by which ,bodies tend towards one
 another1 whatsoever be the ,cause4 ,for
 we must learn from the ,phaenomena of  
,nature what ,bodies attract one        
another1 and what are the ,laws and     
,properties of the ,attraction1 before  
we enquire the ,cause by which the      
,attraction is perform'd4 ,the          
,attractions of ,gravity1 ,magnetism1   
and ,electricity1 reach to very sensible
 distances1 and so have been observed by
 vulgar ,eyes1 and there may be others  
which reach to so small distances as    
hitherto escape ,observation2 and       
perhaps electrical ,attraction may reach
 to such small distances1 even without  
being excited by ,friction4  ,for when  
,salt of ,tartar runs per ,deliquium1 is
 not this done by an ,attraction between
 the ,particles of the ,salt of ,tartar1
 and the ,particles of the ,water which 
float in the ,air in the form of        
,vapours8 ,and why does not common      
,salt1 or ,salt-petre1 or ,vitriol1 run 
per ,deliquium1 but for want of such an 

,attraction8 ,or why does not ,salt of  
,tartar draw more ,water out of the ,air
 than in a certain ,proportion to its   
quantity1 but for want of an attractive 
,force after it is satiated with ,water8
 ,and whence is it but from this        
attractive ,power that ,water which     
alone distils with a gentle luke-warm   
,heat1 will not distil from ,salt of    
,tartar without a great ,heat8 ,and is  
it not from the like attractive ,power  
between the ,particles of ,oil of       
,vitriol and the ,particles of ,water1  
that ,oil of ,vitriol draws to it a good
 quantity of ,water out of the ,air1 and
 after it is satiated draws no more1 and
 in ,distillation lets go the ,water    
very difficultly8 ,and when ,water and  
,oil of ,vitriol poured successively    
into the same ,vessel grow very hot in  
the mixing1 does not this ,heat argue a 
great ,motion in the ,parts of the      
,liquors8 ,and does not this ,motion    
argue1 that the ,parts of the two       
,liquors in mixing coalesce with        

,violence1 and by consequence rush      
towards one another with an accelerated 
,motion8 ,and when ,aqua fortis1 or     
,spirit of ,vitriol poured upon ,filings
 of ,iron dissolves the ,filings with a 
great ,heat and ,ebullition1 is not this
 ,heat and ,ebullition effected by a    
violent ,motion of the ,parts1 and does 
not that ,motion argue that the acid    
,parts of the ,liquor rush towards the  
,parts of the ,metal with violence1 and 
run forcibly into its ,pores till they  
get between its outmost ,particles1 and 
the main ,mass of the ,metal1 and       
surrounding those ,particles loosen them
 from the main ,mass1 and set them at   
liberty to float off into the ,water8   
,and when the acid ,particles1 which    
alone would distil with an easy ,heat1  
will not separate from the ,particles of
 the ,metal without a very violent      
,heat1 does not this confirm the        
,attraction between them8  ,when ,spirit
 of ,vitriol poured upon common ,salt or
 ,salt-petre makes an ,ebullition with  

the ,salt1 and unites with it1 and in   
,distillation the ,spirit of the common 
,salt or ,salt-petre comes over much    
easier than it would do before1 and the 
acid part of the ,spirit of ,vitriol    
stays behind2 does not this argue that  
the fix'd ,alcaly of the ,salt attracts 
the acid ,spirit of the ,vitriol more   
strongly than its own ,spirit1 and not  
being able to hold them both1 lets go   
its own8 ,and when ,oil of ,vitriol is  
drawn off from its weight of ,nitre1 and
 from both the ,ingredients a compound  
,spirit of ,nitre is distilled1 and two 
parts of this ,spirit are poured on one 
part of ,oil of ,cloves or ,carraway    
,seeds1 or of any ponderous ,oil of     
vegetable or animal ,substances1 or ,oil
 of ,turpentine thicken'd with a little 
,balsam of ,sulphur1 and the ,liquors   
grow so very hot in mixing1 as presently
 to send up a burning ,flame2 does not  
this very great and sudden ,heat argue  
that the two ,liquors mix with violence1
 and that their ,parts in mixing run    

towards one another with an accelerated 
,motion1 and clash with the greatest    
,force8 ,and is it not for the same     
reason that well rectified ,spirit of   
,wine poured on the same compound       
,spirit flashes2 and that the ,pulvis   
fulminans1 composed of ,sulphur1 ,nitre1
 and ,salt of ,tartar1 goes off with a  
more sudden and violent ,explosion than 
,gun-powder1 the acid ,spirits of the   
,sulphur and ,nitre rushing towards one 
another1 and towards the ,salt of       
,tartar1 with so great a violence1 as by
 the shock to turn the whole at once    
into ,vapour and ,flame8 ,where the     
,dissolution is slow1 it makes a slow   
,ebullition and a gentle ,heat2 and     
where it is quicker1 it makes a greater 
,ebullition with more heat2 and where it
 is done at once1 the ,ebullition is    
contracted into a sudden ,blast or      
violent ,explosion1 with a heat equal to
 that of ,fire and ,flame4 ,so when a   
,drachm of the above-mention'd compound 
,spirit of ,nitre was poured upon half a

 ,drachm of ,oil of ,carraway ,seeds in 
vacuo1 the ,mixture immediately made a  
flash like ,gun-powder1 and burst the   
exhausted ,receiver1 which was a ,glass 
six ,inches wide1 and eight ,inches     
deep4 ,and even the gross ,body of      
,sulphur powder'd1 and with an equal    
weight of ,iron ,filings and a little   
,water made into ,paste1 acts upon the  
,iron1 and in five or six hours grows   
too hot to be touch'd1 and emits a      
,flame4 ,and by these ,experiments      
compared with the great quantity of     
,sulphur with which the ,earth abounds1 
and the warmth of the interior ,parts of
 the ,earth1 and hot ,springs1 and      
burning ,mountains1 and with ,damps1    
mineral ,coruscations1 ,earthquakes1 hot
 suffocating ,exhalations1 ,hurricanes1 
and ,spouts2 we may learn that          
sulphureous ,steams abound in the       
,bowels of the ,earth and ferment with  
,minerals1 and sometimes take fire with 
a sudden ,coruscation and ,explosion2   
and if pent up in subterraneous         

,caverns1 burst the ,caverns with a     
great shaking of the ,earth1 as in      
springing of a ,mine4 ,and then the     
,vapour generated by the ,explosion1    
expiring through the ,pores of the      
,earth1 feels hot and suffocates1 and   
makes ,tempests and ,hurricanes1 and    
sometimes causes the ,land to slide1 or 
the ,sea to boil1 and carries up the    
,water thereof in ,drops1 which by their
 weight fall down again in ,spouts4     
,also some sulphureous ,steams1 at all  
times when the ,earth is dry1 ascending 
into the ,air1 ferment there with       
nitrous ,acids1 and sometimes taking    
fire cause ,lightning and ,thunder1 and 
fiery ,meteors4 ,for the ,air abounds   
with acid ,vapours fit to promote       
,fermentations1 as appears by the       
rusting of ,iron and ,copper in it1 the 
kindling of ,fire by blowing1 and the   
beating of the ,heart by means of       
,respiration4 ,now the above-mention'd  
,motions are so great and violent as to 
shew that in ,fermentations the         

,particles of ,bodies which almost rest1
 are put into new ,motions by a very    
potent ,principle1 which acts upon them 
only when they approach one another1 and
 causes them to meet and clash with     
great violence1 and grow hot with the   
motion1 and dash one another into       
pieces1 and vanish into ,air1 and       
,vapour1 and ,flame4  ,when ,salt of    
,tartar per deliquium1 being poured into
 the ,solution of any ,metal1           
precipitates the ,metal and makes it    
fall down to the bottom of the ,liquor  
in the form of ,mud3 ,does not this     
argue that the acid ,particles are      
attracted more strongly by the ,salt of 
,tartar than by the ,metal1 and by the  
stronger ,attraction go from the ,metal 
to the ,salt of ,tartar8 ,and so when a 
,solution of ,iron in ,aqua fortis      
dissolves the ,lapis ,calaminaris1 and  
lets go the ,iron1 or a ,solution of    
,copper dissolves ,iron immersed in it  
and lets go the ,copper1 or a ,solution 
of ,silver dissolves ,copper and lets go

 the ,silver1 or a ,solution of ,mercury
 in ,aqua fortis being poured upon      
,iron1 ,copper1 ,tin1 or ,lead1         
dissolves the ,metal and lets go the    
,mercury2 does not this argue that the  
acid ,particles of the ,aqua fortis are 
attracted more strongly by the ,lapis   
,calaminaris than by ,iron1 and more    
strongly by ,iron than by ,copper1 and  
more strongly by ,copper than by        
,silver1 and more strongly by ,iron1    
,copper1 ,tin1 and ,lead1 than by       
,mercury8 ,and is it not for the same   
reason that ,iron requires more ,aqua   
fortis to dissolve it than ,copper1 and 
,copper more than the other ,metals2 and
 that of all ,metals1 ,iron is dissolved
 most easily1 and is most apt to rust2  
and next after ,iron1 ,copper8  ,when   
,oil of ,vitriol is mix'd with a little 
,water1 or is run per deliquium1 and in 
,distillation the ,water ascends        
difficultly1 and brings over with it    
some part of the ,oil of ,vitriol in the
 form of ,spirit of ,vitriol1 and this  

,spirit being poured upon ,iron1        
,copper1 or ,salt of ,tartar1 unites    
with the ,body and lets go the ,water2  
doth not this shew that the acid ,spirit
 is attracted by the ,water1 and more   
attracted by the fix'd ,body than by the
 ,water1 and therefore lets go the      
,water to close with the fix'd ,body8   
,and is it not for the same reason that 
the ,water and acid ,spirits which are  
mix'd together in ,vinegar1 ,aqua       
fortis1 and ,spirit of ,salt1 cohere and
 rise together in ,distillation2 but if 
the ,menstruum be poured on ,salt of    
,tartar1 or on ,lead1 or ,iron1 or any  
fix'd ,body which it can dissolve1 the  
,acid by a stronger ,attraction adheres 
to the ,body1 and lets go the ,water8   
,and is it not also from a mutual       
,attraction that the ,spirits of ,soot  
and ,sea-,salt unite and compose the    
,particles of ,sal-armoniac1 which are  
less volatile than before1 because      
grosser and freer from ,water2 and that 
the ,particles of ,sal-armoniac in      

,sublimation carry up the ,particles of 
,antimony1 which will not sublime alone2
 and that the ,particles of ,mercury    
uniting with the acid ,particles of     
,spirit of ,salt compose ,mercury       
sublimate1 and with the ,particles of   
,sulphur1 compose ,cinnaber2 and that   
the ,particles of ,spirit of ,wine and  
,spirit of ,urine well rectified unite1 
and letting go the ,water which         
dissolved them1 compose a consistent    
,body2 and that in subliming ,cinnaber  
from ,salt of ,tartar1 or from quick    
,lime1 the ,sulphur by a stronger       
,attraction of the ,salt or ,lime lets  
go the ,mercury1 and stays with the     
fix'd ,body2 and that when ,mercury     
sublimate is sublimed from ,antimony1 or
 from ,regulus of ,antimony1 the ,spirit
 of ,salt lets go the ,mercury1 and     
unites with the antimonial metal which  
attracts it more strongly1 and stays    
with it till the ,heat be great enough  
to make them both ascend together1 and  
then carries up the ,metal with it in   

the form of a very fusible ,salt1 called
 ,butter of ,antimony1 although the     
,spirit of ,salt alone be almost as     
volatile as ,water1 and the ,antimony   
alone as fix'd as ,lead8  ,when ,aqua   
fortis dissolves ,silver and not ,gold1 
and ,aqua regia dissolves ,gold and not 
,silver1 may it not be said that ,aqua  
fortis is subtil enough to penetrate    
,gold as well as ,silver1 but wants the 
attractive ,force to give it ,entrance2 
and that ,aqua regia is subtil enough to
 penetrate ,silver as well as ,gold1 but
 wants the attractive ,force to give it 
,entrance8 ,for ,aqua regia is nothing  
else than ,aqua fortis mix'd with some  
,spirit of ,salt1 or with ,sal-armoniac2
 and even common ,salt dissolved in     
,aqua fortis1 enables the ,menstruum to 
dissolve ,gold1 though the ,salt be a   
gross ,body4 ,when therefore ,spirit of 
,salt precipitates ,silver out of ,aqua 
fortis1 is it not done by attracting and
 mixing with the ,aqua fortis1 and not  
attracting1 or perhaps repelling        

,silver8 ,and when ,water precipitates  
,antimony out of the ,sublimate of      
,antimony and ,sal-armoniac1 or out of  
,butter of ,antimony1 is it not done by 
its dissolving1 mixing with1 and        
weakening the ,sal-armoniac or ,spirit  
of ,salt1 and its not attracting1 or    
perhaps repelling the ,antimony8 ,and is
 it not for want of an attractive virtue
 between the ,parts of ,water and ,oil1 
of ,quick-silver and ,antimony1 of ,lead
 and ,iron1 that these ,substances do   
not mix2 and by a weak ,attraction1 that
 ,quick-silver and ,copper mix          
difficultly2 and from a strong one1 that
 ,quick-silver and ,tin1 ,antimony and  
,iron1 ,water and ,salts1 mix readily8  
,and in general1 is it not from the same
 ,principle that ,heat congregates      
homogeneal ,bodies1 and separates       
heterogeneal ones8  ,when ,arsenick with
 ,soap gives a ,regulus1 and with       
,mercury sublimate a volatile fusible   
,salt1 like ,butter of ,antimony1 doth  
not this shew that ,arsenick1 which is a

 ,substance totally volatile1 is        
compounded of fix'd and volatile ,parts1
 strongly cohering by a mutual          
,attraction1 so that the volatile will  
not ascend without carrying up the      
fixed8 ,and so1 when an equal weight of 
,spirit of ,wine and ,oil of ,vitriol   
are digested together1 and in           
,distillation yield two fragrant and    
volatile ,spirits which will not mix    
with one another1 and a fix'd black     
,earth remains behind2 doth not this    
shew that ,oil of ,vitriol is composed  
of volatile and fix'd ,parts strongly   
united by ,attraction1 so as to ascend  
together in form of a volatile1 acid1   
fluid ,salt1 until the ,spirit of ,wine 
attracts and separates the volatile     
,parts from the fixed8 ,and therefore1  
since ,oil of ,sulphur per ,campanam is 
of the same ,nature with ,oil of        
,vitriol1 may it not be inferred1 that  
,sulphur is also a mixture of volatile  
and fix'd ,parts so strongly cohering by
 ,attraction1 as to ascend together in  

,sublimation4 ,by dissolving ,flowers of
 ,sulphur in ,oil of ,turpentine1 and   
distilling the ,solution1 it is found   
that ,sulphur is composed of an         
inflamable thick ,oil or fat ,bitumen1  
an acid ,salt1 a very fix'd ,earth1 and 
a little ,metal4 ,the three first were  
found not much unequal to one another1  
the fourth in so small a quantity as    
scarce to be worth considering4 ,the    
acid ,salt dissolved in ,water1 is the  
same with ,oil of ,sulphur per          
,campanam1 and abounding much in the    
,bowels of the ,earth1 and particularly 
in ,markasites1 unites it self to the   
other ,ingredients of the ,markasite1   
which are1 ,bitumen1 ,iron1 ,copper1 and
 ,earth1 and with them compounds ,allum1
 ,vitriol1 and ,sulphur4 ,with the      
,earth alone it compounds ,allum2 with  
the ,metal alone1 or ,metal and ,earth  
together1 it compounds ,vitriol2 and    
with the ,bitumen and ,earth it         
compounds ,sulphur4 ,whence it comes to 
pass that ,markasites abound with those 

three ,minerals4 ,and is it not from the
 mutual ,attraction of the ,ingredients 
that they stick together for compounding
 these ,minerals1 and that the ,bitumen 
carries up the other ,ingredients of the
 ,sulphur1 which without it would not   
sublime8 ,and the same ,question may be 
put concerning all1 or almost all the   
gross ,bodies in ,nature4 ,for all the  
,parts of ,animals and ,vegetables are  
composed of ,substances volatile and    
fix'd1 fluid and solid1 as appears by   
their ,analysis2 and so are ,salts and  
,minerals1 so far as ,chymists have been
 hitherto able to examine their         
,composition4  ,when ,mercury sublimate 
is re-sublimed with fresh ,mercury1 and 
becomes ,mercurius ,dulcis1 which is a  
white tasteless ,earth scarce           
dissolvable in ,water1 and ,mercurius   
,dulcis re-sublimed with ,spirit of     
,salt returns into ,mercury sublimate2  
and when ,metals corroded with a little 
acid turn into rust1 which is an ,earth 
tasteless and indissolvable in ,water1  

and this ,earth imbibed with more acid  
becomes a metallick ,salt2 and when some
 ,stones1 as ,spar of ,lead1 dissolved  
in proper ,menstruums become ,salts2 do 
not these things shew that ,salts are   
dry ,earth and watry ,acid united by    
,attraction1 and that the ,earth will   
not become a ,salt without so much acid 
as makes it dissolvable in ,water8 ,do  
not the sharp and pungent ,tastes of    
,acids arise from the strong ,attraction
 whereby the acid ,particles rush upon  
and agitate the ,particles of the       
,tongue8 ,and when ,metals are dissolved
 in acid ,menstruums1 and the ,acids in 
conjunction with the ,metal act after a 
different manner1 so that the ,compound 
has a different ,taste much milder than 
before1 and sometimes a sweet one2 is it
 not because the ,acids adhere to the   
metallick ,particles1 and thereby lose  
much of their ,activity8 ,and if the    
,acid be in too small a ,proportion to  
make the ,compound dissolvable in       
,water1 will it not by adhering strongly

 to the ,metal become unactive and lose 
its ,taste1 and the ,compound be a      
tasteless ,earth8 ,for such things as   
are not dissolvable by the ,moisture of 
the ,tongue1 act not upon the ,taste4   
,as ,gravity makes the ,sea flow round  
the denser and weightier ,parts of the  
,globe of the ,earth1 so the ,attraction
 may make the watry ,acid flow round the
 denser and compacter ,particles of     
,earth for composing the ,particles of  
,salt4 ,for otherwise the ,acid would   
not do the ,office of a ,medium between 
the ,earth and common ,water1 for making
 ,salts dissolvable in the ,water2 nor  
would ,salt of ,tartar readily draw off 
the ,acid from dissolved ,metals1 nor   
,metals the ,acid from ,mercury4 ,now1  
as in the great ,globe of the ,earth and
 ,sea1 the densest ,bodies by their     
,gravity sink down in ,water1 and always
 endeavour to go towards the ,center of 
the ,globe2 so in ,particles of ,salt1  
the densest ,matter may always endeavour
 to approach the ,center of the         

,particle3 ,so that a ,particle of ,salt
 may be compared to a ,chaos2 being     
dense1 hard1 dry1 and earthy in the     
,center2 and rare1 soft1 moist1 and     
watry in the ,circumference4 ,and hence 
it seems to be that ,salts are of a     
lasting ,nature1 being scarce destroy'd1
 unless by drawing away their watry     
,parts by violence1 or by letting them  
soak into the ,pores of the central     
,earth by a gentle ,heat in             
,putrefaction1 until the ,earth be      
dissolved by the ,water1 and separated  
into smaller ,particles1 which by reason
 of their ,smallness make the rotten    
,compound appear of a black ,colour4    
,hence also it may be1 that the ,parts  
of ,animals and ,vegetables preserve    
their several ,forms1 and assimilate    
their ,nourishment2 the soft and moist  
,nourishment easily changing its        
,texture by a gentle ,heat and ,motion1 
till it becomes like the dense1 hard1   
dry1 and durable ,earth in the ,center  
of each ,particle4 ,but when the        

,nourishment grows unfit to be          
assimilated1 or the central ,earth grows
 too feeble to assimilate it1 the       
,motion ends in ,confusion1             
,putrefaction1 and ,death4  ,if a very  
small quantity of any ,salt or ,vitriol 
be dissolved in a great quantity of     
,water1 the ,particles of the ,salt or  
,vitriol will not sink to the bottom1   
though they be heavier in ,specie than  
the ,water1 but will evenly diffuse     
themselves into all the ,water1 so as to
 make it as saline at the top as at the 
bottom4 ,and does not this imply that   
the ,parts of the ,salt or ,vitriol     
recede from one another1 and endeavour  
to expand themselves1 and get as far    
asunder as the quantity of ,water in    
which they float1 will allow8 ,and does 
not this ,endeavour imply that they have
 a repulsive ,force by which they fly   
from one another1 or at least1 that they
 attract the ,water more strongly than  
they do one another8 ,for as all things 
ascend in ,water which are less         

attracted than ,water1 by the           
gravitating ,power of the ,earth2 so all
 the ,particles of ,salt which float in 
,water1 and are less attracted than     
,water by any one ,particle of ,salt1   
must recede from that ,particle1 and    
give way to the more attracted ,water4  
,when any saline ,liquor is evaporated  
to a ,cuticle and let cool1 the ,salt   
concretes in regular ,figures2 which    
argues1 that the ,particles of the ,salt
 before they concreted1 floated in the  
,liquor at equal distances in rank and  
file1 and by consequence that they acted
 upon one another by some ,power which  
at equal distances is equal1 at unequal 
distances unequal4 ,for by such a ,power
 they will range themselves uniformly1  
and without it they will float          
irregularly1 and come together as       
irregularly4 ,and since the ,particles  
of ,island-,crystal act all the same way
 upon the ,rays of ,light for causing   
the unusual ,refraction1 may it not be  
supposed that in the ,formation of this 

,crystal1 the ,particles not only ranged
 themselves in rank and file for        
concreting in regular ,figures1 but also
 by some kind of polar ,virtue turned   
their homogeneal ,sides the same way4   
,the ,parts of all homogeneal hard      
,bodies which fully touch one another1  
stick together very strongly4 ,and for  
explaining how this may be1 some have   
invented hooked ,atoms1 which is begging
 the ,question2 and others tell us that 
,bodies are glued together by rest1 that
 is1 by an occult ,quality1 or rather by
 nothing2 and others1 that they stick   
together by conspiring ,motions1 that   
is1 by relative rest amongst themselves4
 ,i had rather infer from their         
,cohesion1 that their ,particles attract
 one another by some ,force1 which in   
immediate ,contact is exceeding strong1 
at small distances performs the chymical
 ,operations above-mention'd1 and       
reaches not far from the ,particles with
 any sensible ,effect4  ,all ,bodies    
seem to be composed of hard ,particles3 

,for otherwise ,fluids would not        
congeal2 as ,water1 ,oils1 ,vinegar1 and
 ,spirit or ,oil of ,vitriol do by      
freezing2 ,mercury by ,fumes of ,lead2  
,spirit of ,nitre and ,mercury1 by      
dissolving the ,mercury and evaporating 
the ,flegm2 ,spirit of ,wine and ,spirit
 of ,urine1 by deflegming and mixing    
them2 and ,spirit of ,urine and ,spirit 
of ,salt1 by subliming them together to 
make ,sal-armoniac4 ,even the ,rays of  
,light seem to be hard ,bodies2 for     
otherwise they would not retain         
different ,properties in their different
 ,sides4 ,and therefore ,hardness may be
 reckon'd the ,property of all          
uncompounded ,matter4 ,at least1 this   
seems to be as evident as the universal 
,impenetrability of ,matter4 ,for all   
,bodies1 so far as ,experience reaches1 
are either hard1 or may be harden'd2 and
 we have no other ,evidence of universal
 ,impenetrability1 besides a large      
,experience without an experimental     
,exception4 ,now if compound ,bodies are

 so very hard as we find some of them to
 be1 and yet are very porous1 and       
consist of ,parts which are only laid   
together2 the simple ,particles which   
are void of ,pores1 and were never yet  
divided1 must be much harder4 ,for such 
hard ,particles being heaped up         
together1 can scarce touch one another  
in more than a few ,points1 and         
therefore must be separable by much less
 ,force than is requisite to break a    
solid ,particle1 whose ,parts touch in  
all the ,space between them1 without any
 ,pores or ,interstices to weaken their 
,cohesion4 ,and how such very hard      
,particles which are only laid together 
and touch only in a few ,points1 can    
stick together1 and that so firmly as   
they do1 without the assistance of      
something which causes them to be       
attracted or press'd towards one        
another1 is very difficult to conceive4 
,the same thing ,i infer also from the  
cohering of two polish'd ,marbles in    
vacuo1 and from the standing of         

,quick-silver in the ,barometer at the  
height of #ej1 #fj or #gj ,inches1 or   
above1 when ever it is well-purged of   
,air and carefully poured in1 so that   
its ,parts be every where contiguous    
both to one another and to the ,glass4  
,the ,atmosphere by its weight presses  
the ,quick-silver into the ,glass1 to   
the height of #bi or #cj ,inches4 ,and  
some other ,agent raises it higher1 not 
by pressing it into the ,glass1 but by  
making its ,parts stick to the ,glass1  
and to one another4 ,for upon any       
discontinuation of ,parts1 made either  
by ,bubbles or by shaking the ,glass1   
the whole ,mercury falls down to the    
height of #bi or #cj ,inches4  ,and of  
the same kind with these ,experiments   
are those that follow4 ,if two plane    
polish'd ,plates of ,glass 7suppose two 
pieces of a polish'd ,looking-glass7 be 
laid together1 so that their sides be   
parallel and at a very small distance   
from one another1 and then their lower  
edges be dipped into ,water1 the ,water 

will rise up between them4 ,and the less
 the distance of the ,glasses is1 the   
greater will be the height to which the 
,water will rise4 ,if the distance be   
about the hundredth part of an ,inch1   
the ,water will rise to the height of   
about an ,inch2 and if the distance be  
greater or less in any ,proportion1 the 
height will be reciprocally proportional
 to the distance very nearly4 ,for the  
attractive ,force of the ,glasses is the
 same1 whether the distance between them
 be greater or less2 and the weight of  
the ,water drawn up is the same1 if the 
height of it be reciprocally            
proportional to the distance of the     
,glasses4 ,and in like manner1 ,water   
ascends between two ,marbles polish'd   
plane1 when their polish'd sides are    
parallel1 and at a very little distance 
from one another1 ,and if slender ,pipes
 of ,glass be dipped at one end into    
stagnating ,water1 the ,water will rise 
up within the ,pipe1 and the height to  
which it rises will be reciprocally     

proportional to the ,diameter of the    
,cavity of the ,pipe1 and will equal the
 height to which it rises between two   
,planes of ,glass1 if the ,semi-diameter
 of the ,cavity of the ,pipe be equal to
 the distance between the ,planes1 or   
thereabouts4 ,and these ,experiments    
succeed after the same manner in vacuo  
as in the open ,air1 7as hath been tried
 before the ,royal ,society17 and       
therefore are not influenced by the     
,weight or ,pressure of the ,atmosphere4
  ,and if a large ,pipe of ,glass be    
filled with sifted ,ashes well pressed  
together in the ,glass1 and one end of  
the ,pipe be dipped into stagnating     
,water1 the ,water will rise up slowly  
in the ,ashes1 so as in the space of a  
,week or ,fortnight to reach up within  
the ,glass1 to the height of #cj or #dj 
,inches above the stagnating ,water4    
,and the ,water rises up to this height 
by the ,action only of those ,particles 
of the ,ashes which are upon the        
,surface of the elevated ,water2 the    

,particles which are within the ,water1 
attracting or repelling it as much      
downwards as upwards4 ,and therefore the
 ,action of the ,particles is very      
strong4 ,but the ,particles of the      
,ashes being not so dense and close     
together as those of ,glass1 their      
,action is not so strong as that of     
,glass1 which keeps ,quick-silver       
suspended to the height of #fj or #gj   
,inches1 and therefore acts with a      
,force which would keep ,water suspended
 to the height of above #fj ,feet4  ,by 
the same ,principle1 a ,sponge sucks in 
,water1 and the ,glands in the ,bodies  
of ,animals1 according to their several 
,natures and ,dispositions1 suck in     
various ,juices from the ,blood4  ,if   
two plane polish'd ,plates of ,glass    
three or four ,inches broad1 and twenty 
or twenty five long1 be laid one of them
 parallel to the ,horizon1 the other    
upon the first1 so as at one of their   
ends to touch one another1 and contain  
an ,angle of about #aj or #ae ,minutes1 

and the same be first moisten'd on their
 inward sides with a clean ,cloth dipp'd
 into ,oil of ,oranges or ,spirit of    
,turpentine1 and a ,drop or two of the  
,oil or ,spirit be let fall upon the    
lower ,glass at the other2 so soon as   
the upper ,glass is laid down upon the  
lower1 so as to touch it at one end as  
above1 and to touch the ,drop at the    
other end1 making with the lower ,glass 
an ,angle of about #aj or #ae ,minutes2 
the ,drop will begin to move towards the
 ,concourse of the ,glasses1 and will   
continue to move with an accelerated    
,motion1 till it arrives at that        
,concourse of the ,glasses4 ,for the two
 ,glasses attract the ,drop1 and make it
 run that way towards which the         
,attractions incline4 ,and if when the  
,drop is in motion you lift up that end 
of the ,glasses where they meet1 and    
towards which the ,drop moves1 the ,drop
 will ascend between the ,glasses1 and  
therefore is attracted4 ,and as you lift
 up the ,glasses more and more1 the     

,drop will ascend slower and slower1 and
 at length rest1 being then carried     
downward by its ,weight1 as much as     
upwards by the ,attraction4 ,and by this
 means you may know the ,force by which 
the ,drop is attracted at all distances 
from the ,concourse of the ,glasses4    
,now by some ,experiments of this kind1 
7made by ,mr4 ,hauksbee7 it has been    
found that the ,attraction is almost    
reciprocally in a duplicate ,proportion 
of the distance of the middle of the    
,drop from the ,concourse of the        
,glasses1 viz4 reciprocally in a simple 
,proportion1 by reason of the spreading 
of the ,drop1 and its touching each     
,glass in a larger ,surface2 and again  
reciprocally in a simple ,proportion1 by
 reason of the ,attractions growing     
stronger within the same quantity of    
attracting ,surface4 ,the ,attraction   
therefore within the same quantity of   
attracting ,surface1 is reciprocally as 
the distance between the ,glasses4 ,and 
therefore where the distance is         

exceeding small1 the ,attraction must be
 exceeding great4 ,by the ,table in the 
second ,part of the second ,book1       
wherein the thicknesses of colour'd     
,plates of ,water between two ,glasses  
are set down1 the thickness of the      
,plate where it appears very black1 is  
three eighths of the ten hundred        
thousandth part of an ,inch4 ,and where 
the ,oil of ,oranges between the        
,glasses is of this thickness1 the      
,attraction collected by the foregoing  
,rule1 seems to be so strong1 as within 
a ,circle of an ,inch in diameter1 to   
suffice to hold up a ,weight equal to   
that of a ,cylinder of ,water of an     
,inch in diameter1 and two or three     
,furlongs in length4 ,and where it is of
 a less thickness the ,attraction may be
 proportionally greater1 and continue to
 increase1 until the thickness do not   
exceed that of a single ,particle of the
 ,oil4 ,there are therefore ,agents in  
,nature able to make the ,particles of  
,bodies stick together by very strong   

,attractions4 ,and it is the ,business  
of experimental ,philosophy to find them
 out4  ,now the smallest ,particles of  
,matter may cohere by the strongest     
,attractions1 and compose bigger        
,particles of weaker ,virtue2 and many  
of these may cohere and compose bigger  
,particles whose ,virtue is still       
weaker1 and so on for divers            
,successions1 until the ,progression end
 in the biggest ,particles on which the 
,operations in ,chymistry1 and the      
,colours of natural ,bodies depend1 and 
which by cohering compose ,bodies of a  
sensible ,magnitude4 ,if the ,body is   
compact1 and bends or yields inward to  
,pression without any sliding of its    
,parts1 it is hard and elastick1        
returning to its ,figure with a ,force  
rising from the mutual ,attraction of   
its ,parts4 ,if the ,parts slide upon   
one another1 the ,body is malleable or  
soft4 ,if they slip easily1 and are of a
 fit ,size to be agitated by ,heat1 and 
the ,heat is big enough to keep them in 

,agitation1 the ,body is fluid2 and if  
it be apt to stick to things1 it is     
humid2 and the ,drops of every fluid    
affect a round ,figure by the mutual    
,attraction of their ,parts1 as the     
,globe of the ,earth and ,sea affects a 
round ,figure by the mutual ,attraction 
of its ,parts by ,gravity4  ,since      
,metals dissolved in ,acids attract but 
a small quantity of the ,acid1 their    
attractive ,force can reach but to a    
small distance from them4 ,and as in    
,algebra1 where affirmative ,quantities 
vanish and cease1 there negative ones   
begin2 so in ,mechanicks1 where         
,attraction ceases1 there a repulsive   
,virtue ought to succeed4 ,and that     
there is such a ,virtue1 seems to follow
 from the ,reflexions and ,inflexions of
 the ,rays of ,light4 ,for the ,rays are
 repelled by ,bodies in both these      
,cases1 without the immediate ,contact  
of the reflecting or inflecting ,body4  
,it seems also to follow from the       
,emission of ,light2 the ,ray so soon as

 it is shaken off from a shining ,body  
by the vibrating ,motion of the ,parts  
of the ,body1 and gets beyond the reach 
of ,attraction1 being driven away with  
exceeding great ,velocity4 ,for that    
,force which is sufficient to turn it   
back in ,reflexion1 may be sufficient to
 emit it4 ,it seems also to follow from 
the ,production of ,air and ,vapour4    
,the ,particles when they are shaken off
 from ,bodies by ,heat or ,fermentation1
 so soon as they are beyond the reach of
 the ,attraction of the ,body1 receding 
from it1 and also from one another with 
great ,strength1 and keeping at a       
distance1 so as sometimes to take up    
above a ,million of ,times more space   
than they did before in the form of a   
dense ,body4 ,which vast ,contraction   
and ,expansion seems unintelligible1 by 
feigning the ,particles of ,air to be   
springy and ramous1 or rolled up like   
,hoops1 or by any other means than a    
repulsive ,power4 ,the ,particles of    
,fluids which do not cohere too         

strongly1 and are of such a ,smallness  
as renders them most susceptible of     
those ,agitations which keep ,liquors in
 a ,fluor1 are most easily separated and
 rarified into ,vapour1 and in the      
,language of the ,chymists1 they are    
volatile1 rarifying with an easy ,heat1 
and condensing with ,cold4 ,but those   
which are grosser1 and so less          
susceptible of ,agitation1 or cohere by 
a stronger ,attraction1 are not         
separated without a stronger ,heat1 or  
perhaps not without ,fermentation4 ,and 
these last are the ,bodies which        
,chymists call fix'd1 and being rarified
 by ,fermentation1 become true permanent
 ,air2 those ,particles receding from   
one another with the greatest ,force1   
and being most difficultly brought      
together1 which upon ,contact cohere    
most strongly4 ,and because the         
,particles of permanent ,air are        
grosser1 and arise from denser          
,substances than those of ,vapours1     
thence it is that true ,air is more     

ponderous than ,vapour1 and that a moist
 ,atmosphere is lighter than a dry one1 
quantity for quantity4 ,from the same   
repelling ,power it seems to be that    
,flies walk upon the ,water without     
wetting their ,feet2 and that the       
,object-glasses of long ,telescopes lie 
upon one another without touching2 and  
that dry ,powders are difficultly made  
to touch one another so as to stick     
together1 unless by melting them1 or    
wetting them with ,water1 which by      
exhaling may bring them together2 and   
that two polish'd ,marbles1 which by    
immediate ,contact stick together1 are  
difficultly brought so close together as
 to stick4  ,and thus ,nature will be   
very conformable to her self and very   
simple1 performing all the great        
,motions of the heavenly ,bodies by the 
,attraction of ,gravity which intercedes
 those ,bodies1 and almost all the small
 ones of their ,particles by some other 
attractive and repelling ,powers which  
intercede the ,particles4 ,the ,vis     

inertiae is a passive ,principle by     
which ,bodies persist in their ,motion  
or ,rest1 receive ,motion in proportion 
to the ,force impressing it1 and resist 
as much as they are resisted4 ,by this  
,principle alone there never could have 
been any ,motion in the ,world4 ,some   
other ,principle was necessary for      
putting ,bodies into ,motion2 and now   
they are in ,motion1 some other         
,principle is necessary for conserving  
the ,motion4 ,for from the various      
,composition of two ,motions1 'tis very 
certain that there is not always the    
same quantity of ,motion in the ,world4 
,for if two ,globes joined by a slender 
,rod1 revolve about their common ,center
 of ,gravity with an uniform ,motion1   
while that ,center moves on uniformly in
 a right ,line drawn in the ,plane of   
their circular ,motion2 the ,sum of the 
,motions of the two ,globes1 as often as
 the ,globes are in the right ,line     
described by their common ,center of    
,gravity1 will be bigger than the ,sum  

of their ,motions1 when they are in a   
,line perpendicular to that right ,line4
 ,by this ,instance it appears that     
,motion may be got or lost4 ,but by     
reason of the ,tenacity of ,fluids1 and 
,attrition of their ,parts1 and the     
,weakness of ,elasticity in ,solids1    
,motion is much more apt to be lost than
 got1 and is always upon the ,decay4    
,for ,bodies which are either absolutely
 hard1 or so soft as to be void of      
,elasticity1 will not rebound from one  
another4 ,impenetrability makes them    
only stop4 ,if two equal ,bodies meet   
directly in vacuo1 they will by the     
,laws of ,motion stop where they meet1  
and lose all their ,motion1 and remain  
in rest1 unless they be elastick1 and   
receive new ,motion from their ,spring4 
,if they have so much ,elasticity as    
suffices to make them re-bound with a   
quarter1 or half1 or three quarters of  
the ,force with which they come         
together1 they will lose three quarters1
 or half1 or a quarter of their ,motion4

 ,and this may be try'd1 by letting two 
equal ,pendulums fall against one       
another from equal heights4 ,if the     
,pendulums be of ,lead or soft ,clay1   
they will lose all or almost all their  
,motions3 ,if of elastick ,bodies they  
will lose all but what they recover from
 their ,elasticity4 ,if it be said1 that
 they can lose no ,motion but what they 
communicate to other ,bodies1 the       
consequence is1 that in vacuo they can  
lose no ,motion1 but when they meet they
 must go on and penetrate one another's 
,dimensions4 ,if three equal round      
,vessels be filled1 the one with ,water1
 the other with ,oil1 the third with    
molten ,pitch1 and the ,liquors be      
stirred about alike to give them a      
vortical ,motion2 the ,pitch by its     
,tenacity will lose its ,motion quickly1
 the ,oil being less tenacious will keep
 it longer1 and the ,water being less   
tenacious will keep it longest1 but yet 
will lose it in a short time4 ,whence it
 is easy to understand1 that if many    

contiguous ,vortices of molten ,pitch   
were each of them as large as those     
which some suppose to revolve about the 
,sun and fix'd ,stars1 yet these and all
 their ,parts would1 by their ,tenacity 
and ,stiffness1 communicate their       
,motion to one another till they all    
rested among themselves4 ,vortices of   
,oil or ,water1 or some fluider ,matter1
 might continue longer in ,motion2 but  
unless the ,matter were void of all     
,tenacity and ,attrition of ,parts1 and 
,communication of ,motion1 7which is not
 to be supposed17 the ,motion would     
constantly decay4 ,seeing therefore the 
variety of ,motion which we find in the 
,world is always decreasing1 there is a 
necessity of conserving and recruiting  
it by active ,principles1 such as are   
the cause of ,gravity1 by which ,planets
 and ,comets keep their ,motions in     
their ,orbs1 and ,bodies acquire great  
,motion in falling2 and the cause of    
,fermentation1 by which the ,heart and  
,blood of ,animals are kept in perpetual

 ,motion and ,heat2 the inward ,parts of
 the ,earth are constantly warm'd1 and  
in some places grow very hot2 ,bodies   
burn and shine1 ,mountains take fire1   
the ,caverns of the ,earth are blown up1
 and the ,sun continues violently hot   
and lucid1 and warms all things by his  
,light4 ,for we meet with very little   
,motion in the ,world1 besides what is  
owing to these active ,principles4 ,and 
if it were not for these ,principles1   
the ,bodies of the ,earth1 ,planets1    
,comets1 ,sun1 and all things in them1  
would grow cold and freeze1 and become  
inactive ,masses2 and all ,putrefaction1
 ,generation1 ,vegetation and ,life     
would cease1 and the ,planets and       
,comets would not remain in their ,orbs4
  ,all these things being consider'd1 it
 seems probable to me1 that ,god in the 
,beginning form'd ,matter in solid1     
massy1 hard1 impenetrable1 moveable     
,particles1 of such ,sizes and ,figures1
 and with such other ,properties1 and in
 such ,proportion to ,space1 as most    

conduced to the ,end for which he form'd
 them2 and that these primitive         
,particles being ,solids1 are           
incomparably harder than any porous     
,bodies compounded of them2 even so very
 hard1 as never to wear or break in     
pieces2 no ordinary ,power being able to
 divide what ,god himself made one in   
the first ,creation4 ,while the         
,particles continue entire1 they may    
compose ,bodies of one and the same     
,nature and ,texture in all ,ages3 ,but 
should they wear away1 or break in      
pieces1 the ,nature of ,things depending
 on them1 would be changed4 ,water and  
,earth1 composed of old worn ,particles 
and ,fragments of ,particles1 would not 
be of the same ,nature and ,texture now1
 with ,water and ,earth composed of     
entire ,particles in the ,beginning4    
,and therefore1 that ,nature may be     
lasting1 the ,changes of corporeal      
,things are to be placed only in the    
various ,separations and new            
,associations and ,motions of these     

permanent ,particles2 compound ,bodies  
being apt to break1 not in the midst of 
solid ,particles1 but where those       
,particles are laid together1 and only  
touch in a few ,points4  ,it seems to me
 farther1 that these ,particles have not
 only a ,vis inertiae1 accompanied with 
such passive ,laws of ,motion as        
naturally result from that ,force1 but  
also that they are moved by certain     
active ,principles1 such as is that of  
,gravity1 and that which causes         
,fermentation1 and the ,cohesion of     
,bodies4 ,these ,principles ,i consider1
 not as occult ,qualities1 supposed to  
result from the specifick ,forms of     
,things1 but as general ,laws of        
,nature1 by which the ,things themselves
 are form'd2 their ,truth appearing to  
us by ,phaenomena1 though their ,causes 
be not yet discover'd4 ,for these are   
manifest ,qualities1 and their ,causes  
only are occult4 ,and the ,aristotelians
 gave the ,name of occult ,qualities1   
not to manifest ,qualities1 but to such 

,qualities only as they supposed to lie 
hid in ,bodies1 and to be the unknown   
,causes of manifest ,effects3 ,such as  
would be the ,causes of ,gravity1 and of
 magnetick and electrick ,attractions1  
and of ,fermentations1 if we should     
suppose that these ,forces or ,actions  
arose from ,qualities unknown to us1 and
 uncapable of being discovered and made 
manifest4 ,such occult ,qualities put a 
stop to the ,improvement of natural     
,philosophy1 and therefore of late      
,years have been rejected4 ,to tell us  
that every ,species of ,things is       
endow'd with an occult specifick        
,quality by which it acts and produces  
manifest ,effects1 is to tell us        
nothing3 ,but to derive two or three    
general ,principles of ,motion from     
,phaenomena1 and afterwards to tell us  
how the ,properties and ,actions of all 
corporeal ,things follow from those     
manifest ,principles1 would be a very   
great step in ,philosophy1 though the   
,causes of those ,principles were not   

yet discover'd3 ,and therefore ,i       
scruple not to propose the ,principles  
of ,motion above-mention'd1 they being  
of very general ,extent1 and leave their
 ,causes to be found out4  ,now by the  
help of these ,principles1 all material 
,things seem to have been composed of   
the hard and solid ,particles           
above-mention'd1 variously associated in
 the first ,creation by the ,counsel of 
an intelligent ,agent4 ,for it became   
him who created them to set them in     
order4 ,and if he did so1 it's          
unphilosophical to seek for any other   
,origin of the ,world1 or to pretend    
that it might arise out of a ,chaos by  
the mere ,laws of ,nature2 though being 
once form'd1 it may continue by those   
,laws for many ,ages4 ,for while ,comets
 move in very excentrick ,orbs in all   
manner of ,positions1 blind ,fate could 
never make all the ,planets move one and
 the same way in ,orbs concentrick1 some
 inconsiderable ,irregularities         
excepted1 which may have risen from the 

mutual ,actions of ,comets and ,planets 
upon one another1 and which will be apt 
to increase1 till this ,system wants a  
,reformation4 ,such a wonderful         
,uniformity in the ,planetary ,system   
must be allowed the ,effect of ,choice4 
,and so must the ,uniformity in the     
,bodies of ,animals1 they having        
generally a right and a left side shaped
 alike1 and on either side of their     
,bodies two ,legs behind1 and either two
 ,arms1 or two ,legs1 or two ,wings     
before upon their ,shoulders1 and       
between their ,shoulders a ,neck running
 down into a ,back-bone1 and a ,head    
upon it2 and in the ,head two ,ears1 two
 ,eyes1 a ,nose1 a ,mouth1 and a        
,tongue1 alike situated4 ,also the first
 ,contrivance of those very artificial  
,parts of ,animals1 the ,eyes1 ,ears1   
,brain1 ,muscles1 ,heart1 ,lungs1       
,midriff1 ,glands1 ,larynx1 ,hands1     
,wings1 swimming ,bladders1 natural     
,spectacles1 and other ,organs of ,sense
 and ,motion2 and the ,instinct of      

,brutes and ,insects1 can be the effect 
of nothing else than the ,wisdom and    
,skill of a powerful ever-living ,agent1
 who being in all ,places1 is more able 
by his ,will to move the ,bodies within 
his boundless uniform ,sensorium1 and   
thereby to form and reform the ,parts of
 the ,universe1 than we are by our ,will
 to move the ,parts of our own ,bodies4 
,and yet we are not to consider the     
,world as the ,body of ,god1 or the     
several ,parts thereof1 as the ,parts of
 ,god4 ,he is an uniform ,being1 void of
 ,organs1 ,members or ,parts1 and they  
are his ,creatures subordinate to him1  
and subservient to his ,will2 and he is 
no more the ,soul of them1 than the     
,soul of ,man is the ,soul of the       
,species of ,things carried through the 
,organs of ,sense into the place of its 
,sensation1 where it perceives them by  
means of its immediate ,presence1       
without the ,intervention of any third  
thing4 ,the ,organs of ,sense are not   
for enabling the ,soul to perceive the  

,species of ,things in its ,sensorium1  
but only for conveying them thither2 and
 ,god has no need of such ,organs1 he   
being every where present to the ,things
 themselves4 ,and since ,space is       
divisible in infinitum1 and ,matter is  
not necessarily in all places1 it may be
 also allow'd that ,god is able to      
create ,particles of ,matter of several 
,sizes and ,figures1 and in several     
,proportions to ,space1 and perhaps of  
different ,densities and ,forces1 and   
thereby to vary the ,laws of ,nature1   
and make ,worlds of several sorts in    
several ,parts of the ,universe4 ,at    
least1 ,i see nothing of ,contradiction 
in all this4  ,as in ,mathematicks1 so  
in ,natural ,philosophy1 the            
,investigation of difficult ,things by  
the ,method of ,analysis1 ought ever to 
precede the ,method of ,composition4    
,this ,analysis consists in making      
,experiments and ,observations1 and in  
drawing general ,conclusions from them  
by ,induction1 and admitting of no      

,objections against the ,conclusions1   
but such as are taken from ,experiments1
 or other certain ,truths4 ,for         
,hypotheses are not to be regarded in   
experimental ,philosophy4 ,and although 
the arguing from ,experiments and       
,observations by ,induction be no       
,demonstration of general ,conclusions2 
yet it is the best way of arguing which 
the ,nature of ,things admits of1 and   
may be looked upon as so much the       
stronger1 by how much the ,induction is 
more general4 ,and if no ,exception     
occur from ,phaenomena1 the ,conclusion 
may be pronounced generally4 ,but if at 
any time afterwards any ,exception shall
 occur from ,experiments1 it may then   
begin to be pronounced with such        
,exceptions as occur4 ,by this way of   
,analysis we may proceed from ,compounds
 to ,ingredients1 and from ,motions to  
the ,forces producing them2 and in      
general1 from ,effects to their ,causes1
 and from particular ,causes to more    
general ones1 till the ,argument end in 

the most general4 ,this is the ,method  
of ,analysis3 ,and the ,synthesis       
consists in assuming the ,causes        
discover'd1 and establish'd as          
,principles1 and by them explaining the 
,phaenomena proceeding from them1 and   
proving the ,explanations4  ,in the two 
first ,books of these ,opticks1 ,i      
proceeded by this ,analysis to discover 
and prove the original ,differences of  
the ,rays of ,light in respect of       
,refrangibility1 ,reflexibility1 and    
,colour1 and their alternate ,fits of   
easy ,reflexion and easy ,transmission1 
and the ,properties of ,bodies1 both    
opake and pellucid1 on which their      
,reflexions and ,colours depend4 ,and   
these ,discoveries being proved1 may be 
assumed in the ,method of ,composition  
for explaining the ,phaenomena arising  
from them3 ,an ,instance of which       
,method ,i gave in the ,end of the first
 ,book4 ,in this third ,book ,i have    
only begun the ,analysis of what remains
 to be discover'd about ,light and its  

,effects upon the ,frame of ,nature1    
hinting several things about it1 and    
leaving the ,hints to be examin'd and   
improv'd by the farther ,experiments and
 ,observations of such as are           
inquisitive4 ,and if natural ,philosophy
 in all its ,parts1 by pursuing this    
,method1 shall at length be perfected1  
the ,bounds of ,moral ,philosophy will  
be also enlarged4 ,for so far as we can 
know by natural ,philosophy what is the 
first ,cause1 what ,power he has over   
us1 and what ,benefits we receive from  
him1 so far our ,duty towards him1 as   
well as that towards one another1 will  
appear to us by the ,light of ,nature4  
,and no doubt1 if the ,worship of false 
,gods had not blinded the ,heathen1     
their moral ,philosophy would have gone 
farther than to the four ,cardinal      
,virtues2 and instead of teaching the   
,transmigration of ,souls1 and to       
worship the ,sun and ,moon1 and dead    
,heroes1 they would have taught us to   
worship our true ,author and            

,benefactor1 as their ,ancestors did    
under the ,government of ,noah and his  
,sons before they corrupted themselves4