,a    ,,preliminary ,,dissertation      
,,on ,,the    ,,mechanism ,,of ,,the    
,,heavens4        ,,by    ,,mrs4        
,,sommerville          ,,philadelphia3  
,,carey  ,,lea    #ahcb          ,in    
order to convey some idea of the object 
of this work1 it may be  useful to offer
 a few preliminary observations on the  
nature of the  subject which it is      
intended to investigate1 and of the     
means that have  already been adopted   
with so much success to bring within the
 reach of  our faculties1 those truths  
which might seem to be placed so far    
beyond  them4    ,all the knowledge we  
possess of external objects is founded  
upon  experience1 which furnishes a     
knowledge of facts1 and the comparison  
of  these facts establishes relations1  
from which1 induction1 the intuitive    
belief that like causes will produce    
like effects1 leads us to general  laws4
 ,thus1 experience teaches that bodies  
fall at the surface of the  earth with  
an accelerated velocity1 and            

proportional to their masses4  ,newton  
proved1 by comparison1 that the force   
which occasions the fall of  bodies at  
the earth's surface1 is identical with  
that which retains the  moon in her     
orbit2 and induction led him to conclude
 that as the moon is  kept in her orbit 
by the attraction of the earth1 so the  
planets might  be retained in their     
orbits by the attraction of the sun4 ,by
 such steps  he was led to the discovery
 of one of those powers with which the  
,creator has ordained that matter should
 reciprocally act upon matter4          
,physical astronomy is the science which
 compares and identifies the laws  of   
motion observed on earth with the       
motions that take place in the  heavens1
 and which traces1 by an uninterrupted  
chain of deduction from  the great      
principle that governs the universe1 the
 revolutions and  rotations of the      
planets1 and the oscillations of the    
fluids at their  surfaces1 and which    
estimates the changes the system has    

hitherto  undergone or may hereafter    
experience1 changes which require       
millions of  years for their            
accomplishment4    ,the combined efforts
 of astronomers1 from the earliest dawn 
of  civilization1 have been requisite to
 establish the mechanical theory of     
astronomy3 the courses of the planets   
have been observed for ages with a      
degree of perseverance that is          
astonishing1 if we consider the         
imperfection1 and even the want of      
instruments4 ,the real motions of the   
earth have been separated from the      
apparent motions of the planets2 the    
laws of the planetary revolutions have  
been discovered2 and the  discovery of  
these laws has led to the knowledge of  
the gravitation of  matter4 ,on the     
other hand1 descending from the         
principle of gravitation1  every motion 
in the system of the world has been so  
completely  explained1 that no          
astronomical phenomenon can now be      
transmitted to  posterity of which the  

laws have not been determined4          
,science1 regarded as the pursuit of    
truth1 which can only be attained by    
patient and unprejudiced investigation1 
wherein nothing is too great to  be     
attempted1 nothing so minute as to be   
justly disregarded1 must ever  afford   
occupation of consummate interest and of
 elevated meditation4 ,the              
contemplation of the works of creation  
elevates the mind to the  admiration of 
whatever is great and noble1            
accomplishing the object of  all study1 
which in the elegant language of ,sir   
,james ,mackintosh is to  inspire the   
love of truth1 of wisdom1 of beauty1    
especially of goodness1  the highest    
beauty1 and of that supreme and eternal 
mind1 which contains  all truth and     
wisdom1 all beauty and goodness4 ,by the
 love or delightful  contemplation and  
pursuit of these transcendent aims for  
their own sake  only1 the mind of man is
 raised from low and perishable objects1
 and  prepared for those high destinies 

which are appointed for all those who   
are capable of them4    ,the heavens    
afford the most sublime subject of study
 which can be  derived from science3 the
 magnitude and splendour of the objects1
 the  inconceivable rapidity with which 
they move1 and the enormous distances   
between them1 impress the mind with some
 notion of the energy that  maintains   
them in their motions with a durability 
to which we can see no  limits4 ,equally
 conspicuous is the goodness of the     
great ,first ,cause in  having endowed  
man with faculties by which he can not  
only appreciate  the magnificence of his
 works1 but trace1 with precision1 the  
operation  of his laws1 use the globe he
 inhabits us a base wherewith to measure
  the magnitude and distance of the sun 
and planets1 and make the diameter  of  
the earth's orbit the first step of a   
scale by which he may ascend to  the    
starry firmament4 ,such pursuits1 while 
they ennoble the mind1 at the  same time
 inculcate humility1 by showing that    

there is a barrier1 which  no energy1   
mental or physical1 can ever enable us  
to pass3 that however  profoundly we may
 penetrate the depths of space1 there   
still remain  innumerable systems       
compared with which those which seem so 
mighty to us  must dwindle into         
insignificance1 or even become          
invisible2 and that not  only man1 but  
the globe he inhabits1 nay the whole    
system of which it  forms so small a    
part1 might be annihilated1 and its     
extinction be  unperceived in the       
immensity or creation4    ,a complete   
acquaintance with ,physical ,astronomy  
can only be attained by  those who are  
well versed in the higher branches of   
mathematical and  mechanical science3   
such alone can appreciate the extreme   
beauty of  the results1 and of the means
 by which these results are obtained4   
,nevertheless a sufficient skill in     
analysis to follow the general  outline1
 to see the mutual dependence of the    
different parts of the  system1 and to  

comprehend by what means some of the    
most extraordinary  conclusions have    
been arrived at1 is within the reach of 
many who shrink  from the task1 appalled
 by difficulties1 which perhaps are not 
more  formidable than those incident to 
the study of the elements of every      
branch of knowledge1 and possibly       
overrating them by not making a         
sufficient distinction between the      
degree of mathematical acquirement      
necessary for making discoveries1 and   
that which is requisite for             
understanding what others have done4    
,that the study of mathematics and      
their application to astronomy are full 
of interest will be allowed by  all who 
have devoted their time and attention to
 these pursuits1 and  they only can     
estimate the delight of arriving at     
truth1 whether it be  in the discovery  
of a world1 or of a new property of     
numbers4    ,it has been proved by      
,newton that a particle of matter placed
 without  the surface of a hollow sphere

 is attracted by it in the name manner  
as  if its mass1 or the whole matter it 
contains1 were collected in its  centre4
 ,the same is therefore true of a solid 
sphere which may be  supposed to consist
 of an infinite number of concentric    
hollow spheres4  ,this however is not   
the case with a spheroid1 but the       
celestial bodies  are so nearly         
spherical1 and at such remote distances 
from each other1  that they attract and 
are attracted as if each were a dense   
point  situate in its centre of gravity1
 a circumstance which greatly           
facilitates the investigation of their  
motions4    ,the attraction of the earth
 on bodies at its surface in that       
latitude1  the square of whose sine is 1
 is the same as if it were a sphere2 and
  experience shows that bodies there    
fall through #af4jfig feet in a  second4
 ,the mean distance of the moon from the
 earth is about sixty  times the mean   
radius of the earth4 ,when the number   
#af4jfig is  diminished in the ratio of 

#a to #cfjj1 which is the square of the 
moon's  distance from the earth1 it is  
found to be exactly the space the moon  
would fall through in the first second  
of her descent to the earth1 were  she  
not prevented by her centrifugal force1 
arising from the velocity  with which   
she moves in her orbit4 ,so that the    
moon is retained in her  orbit by a     
force having the same origin and        
regulated by the same law  with that    
which causes a stone to fall at the     
earth's surface4 ,the earth  may        
therefore be regarded as the centre of a
 force which extends to the  moon2 but  
as experience shows that the action and 
reaction of matter are  equal and       
contrary1 the moon must attract the     
earth with an equal and  contrary force4
    ,newton proved that a body projected
 in space will move in a conic  section1
 if it be attracted by a force directed 
towards a fixed point1  and having an   
intensity inversely as the square of the
 distance2 but  that any deviation from 

that law will cause it to move in a     
curve of a  different nature4 ,kepler   
ascertained by direct observation that  
the  planets describe ellipses round the
 sun1 and later observations show  that 
comets also move in conic sections3 it  
consequently follows that  the sun      
attracts all the planets and comets     
inversely as the square of  their       
distances from his centre2 the sun      
therefore is the centre of a  force     
extending indefinitely in space1 and    
including all the bodies of  the system 
in its action4    ,kepler also deduced  
from observation1 that the squares of   
the periodic  times of the planets1 or  
the times of their revolutions round the
 sun1  are proportional to the cubes of 
their mean distances from his centre3   
whence it follows1 that the intensity of
 gravitation of all the bodies  towards 
the sun is the same at equal distances2 
consequently gravitation  is            
proportional to the masses1 for if the  
planets and comets be supposed  to be at

 equal distances from the sun and left  
to the effects of  gravity1 they would  
arrive at his surface at the same time4 
,the  satellites also gravitate to their
 primaries according to the same law    
that their primaries do to the sun4     
,hence1 by the law of action and        
reaction1 each body is itself the centre
 of an attractive force  extending      
indefinitely in space1 whence proceed   
all the mutual  disturbances that render
 the celestial motions so complicated1  
and their  investigation so difficult4  
,the gravitation of matter directed to a
 centre1 and attracting directly  as the
 mass1 and inversely as the square of   
the distance1 does not  belong to it    
when taken in mass2 particle acts on    
particle according to  the same law when
 at sensible distances from each other4 
,if the sun  acted on the centre of the 
earth without attracting each of its    
particles1 the tides would be very much 
greater than they now are1 and  in other
 respects they also would be very       

different4 ,the gravitation of  the     
earth to the sun results from the       
gravitation of all its particles1  which
 in their turn attract the sun in the   
ratio of their respective  masses4      
,there is a reciprocal action likewise  
between the earth and  every particle at
 its surface2 were this not the case1   
and were any  portion of the earth1     
however small1 to attract another       
portion and not  be itself attracted1   
the centre of gravity of the earth would
 be moved  in space1 which is           
impossible4    ,the form of the planets 
results from the reciprocal attraction  
of their  component particles4 ,a       
detached fluid mass1 if at rest1 would  
assume the  form of a sphere1 from the  
reciprocal attraction of its particles2 
but  if the mass revolves about an axis1
 it becomes flattened at the poles1  and
 bulges at the equator1 in consequence  
of the centrifugal force  arising from  
the velocity of rotation4 ,for1 the     
centrifugal force  diminishes the       

gravity of the particles at the equator1
 and equilibrium  can only exist when   
these two forces are balanced by an     
increase of  gravity2 therefore1 as the 
attractive force is the same on all     
particles  at equal distances from the  
centre of a sphere1 the equatorial      
particles  would recede from the centre 
till their increase in number balanced  
the  centrifugal force by their         
attraction1 consequently the sphere     
would  become an oblate spheroid2 and a 
fluid partially or entirely covering a  
solid1 as the ocean and atmosphere cover
 the earth1 must assume that  form in   
order to remain in equilibrio4 ,the     
surface of the sea is  therefore        
spheroidal1 and the surface of the earth
 only deviates from  that figure where  
it rises above or sinks below the level 
of the sea2  but the deviation is so    
small that it is unimportant when       
compared with  the magnitude of the     
earth4 ,such is the form of the earth   
and planets1  but the compression or    

flattening at their poles is so small1  
that even  ,jupiter1 whose rotation is  
the most rapid1 differs but little from 
a  sphere4 ,although the planets attract
 each other as if they were spheres  on 
account of their immense distances1 yet 
the satellites are near  enough to be   
sensibly affected in their motions by   
the forms of their  primaries4 ,the moon
 for example is so near the earth1 that 
the  reciprocal attraction between each 
of her particles and each of the        
particles in the prominent mass at the  
terrestrial equator1 occasions          
considerable disturbances in the motions
 of both bodies4 ,for1 the action  of   
the moon on the matter at the earth's   
equator produces a nutation in  the axis
 of rotation1 and the reaction of that  
matter on the moon is the  cause of a   
corresponding nutation in the lunar     
orbit4    ,if a sphere at rest in space 
receives an impulse passing through its 
centre of gravity1 all its parts will   
move with an equal velocity in a        

straight line2 but if the impulse does  
not pass through the centre of  gravity1
 its particles having unequal           
velocities1 will give it a  rotatory    
motion at the same time that it is      
translated in space4 ,these  motions are
 independent of one another1 so that a  
contrary impulse  passing through its   
centre of gravity will impede its       
progression1  without interfering with  
its rotation4 ,as the sun rotates about 
an axis1  it seems probable if an       
impulse in a contrary direction has not 
been  given to his centre of gravity1   
that he moves in space accompanied by   
all those bodies which compose the solar
 system1 a circumstance that  would in  
no way interfere with their relative    
motions2 for1 in  consequence of our    
experience that force is proportional to
 velocity1  the reciprocal attractions  
of a system remain the same1 whether its
  centre of gravity be at rest1 or      
moving uniformly in space4 ,it is       
computed that had the earth received its

 motion from a single impulse1  such    
impulse must have passed through a point
 about twenty-five miles  from its      
centre4    ,since the motions of the    
rotation and translation of the planets 
are  independent of each other1 though  
probably communicated by the same       
impulse1 they form separate subjects of 
investigation4    ,a planet moves in its
 elliptical orbit with a velocity       
varying every  instant1 in consequence  
of two forces1 one tending to the centre
 of the  sun1 and the other in the      
direction of a tangent to its orbit1    
arising  from the primitive impulse     
given at the time when it was launched  
into  space3 should the force in the    
tangent cease1 the planet would fall to 
the sun by its gravity2 were the sun not
 to attract it1 the planet would  fly   
off in the tangent4 ,thus1 when a planet
 is in its aphelion or at the  point    
where the orbit is farthest from the    
sun1 his action overcomes its  velocity1
 and brings it towards him with such an 

accelerated motion1  that it at last    
overcomes the sun's attraction1 and     
shoots past him2  then1 gradually       
decreasing in velocity1 it arrives at   
the aphelion where  the sun's attraction
 again prevails4 ,in this motion the    
radii vectores1  or imaginary lines     
joining the centres of the sun and      
planets1 pass over  equal areas in equal
 times4    ,if the planets were         
attracted by the sun only1 this would   
ever be their  course2 and because his  
action is proportional to his mass1     
which is  immensely larger than that of 
all the planets put together1 the       
elliptical is the nearest approximation 
to their true motions1 which are        
extremely complicated1 in consequence of
 their mutual attraction1 so  that they 
do not move in any known or symmetrical 
curve1 but in paths  now approaching to1
 and now receding from the elliptical   
form1 and their  radii vectores do not  
describe areas exactly proportional to  
the time4  ,thus the areas become a test

 of the existence of disturbing forces4 
,to determine the motion of each body   
when disturbed by all the rest is       
beyond the power of analysis2 it is     
therefore necessary to estimate the     
disturbing action of one planet at a    
time1 whence arises the celebrated      
problem of the three bodies1 which      
originally was that of the moon1 the    
earth1 and the sun1 namely1--the masses 
being given of three bodies  projected  
from three given points1 with velocities
 given both in  quantity and direction2 
and supposing the bodies to gravitate to
 one  another with forces that are      
directly as their masses1 and inversely 
as  the squares of the distances1 to    
find the lines described by these       
bodies1 and their position at any given 
instant4    ,by this problem the motions
 of translation of all the celestial    
bodies  are determined4 ,it is one of   
extreme difficulty1 and would be of     
infinitely greater difficulty1 if the   
disturbing action were not very  small1 

when compared with the central force4   
,as the disturbing influence  of each   
body may be found separately1 it is     
assumed that the action of  the whole   
system in disturbing any one planet is  
equal to the sum of all  the particular 
disturbances it experiences1 on the     
general mechanical  principle1 that the 
sum of any number of small oscillations 
is nearly  equal to their simultaneous  
and joint effect4    ,on account of the 
reciprocal action of matter1 the        
stability of the  system depends on the 
intensity of the primitive momentum of  
the  planets1 and the ratio of their    
masses to that of the sun3 for the      
nature of the conic sections in which   
the celestial bodies move1 depends  on  
the velocity with which they were first 
propelled in space2 had that  velocity  
been such as to make the planets move in
 orbits of unstable  equilibrium1 their 
mutual attractions might have changed   
them into  parabolas or even hyperbolas2
 so that the earth and planets might    

ages  ago have been sweeping through the
 abyss of space3 but as the orbits      
differ very little from circles1 the    
momentum of the planets when  projected1
 must have been exactly sufficient to   
ensure the permanency  and stability of 
the system4 ,besides the mass of the sun
 is immensely  greater than those of the
 planets2 and as their inequalities bear
 the  same ratio to their elliptical    
motions as their masses do to that of   
the  sun1 their mutual disturbances only
 increase or diminish the               
eccentricities of their orbits by very  
minute quantities2 consequently  the    
magnitude of the sun's mass is the      
principal cause of the stability  of the
 system4 ,there is not in the physical  
world a more splendid  example of the   
adaptation of means to the              
accomplishment of the end1  than is     
exhibited in the nice adjustment of     
these forces4    ,the orbits of the     
planets have a very small inclination to
 the plane of  the ecliptic in which the

 earth moves2 and on that account1      
astronomers  refer their motions to it  
at a given epoch as a known and fixed   
position4 ,the paths of the planets1    
when their mutual disturbances are      
omitted1 are ellipses nearly approaching
 to circles1 whose planes1  slightly    
inclined to the ecliptic3 cut it in     
straight lines passing  through the     
centre of the sun2 the points where the 
orbit intersects the  plane of the      
ecliptic are its nodes4    ,the orbits  
of the recently discovered planets      
deviate more from the  ecliptic3 that of
 ,pallas has an inclination of #ce to   
it3 on that  account it will be more    
difficult to determine their motions4   
,these  little planets have no sensible 
effect in disturbing the rest1 though   
their own motions are rendered very     
irregular by the proximity of  ,jupiter 
and ,saturn4    ,the planets are subject
 to disturbances of two distinct kinds1 
both  resulting from the constant       
operation of their reciprocal           

attraction1  one kind depending upon    
their positions with regard to each     
other1  begins from zero1 increases to a
 maximum1 decreases and becomes zero    
again1 when the planets return to the   
same relative positions4 ,in            
consequence of these1 the troubled      
planet is sometimes drawn away from  the
 sun1 sometimes brought nearer to him2  
at one time it is drawn above  the plane
 of its orbit1 at another time below it1
 according to the  position of the      
disturbing body4 ,all such changes1     
being accomplished in  short periods1   
some in a few months1 others in years1  
or in hundreds of  years1 are           
denominated ,periodic ,inequalities4    
,the inequalities of the other kind1    
though occasioned likewise by the       
disturbing energy of the planets1 are   
entirely independent of their  relative 
positions2 they depend on the relative  
positions of the orbits  alone1 whose   
forms and places in space are altered by
 very minute  quantities in immense     

periods of time1 and are therefore      
called ,secular  ,inequalities4    ,in  
consequence of disturbances of this     
kind1 the apsides1 or extremities  of   
the major axes of all the orbits1 have a
 direct1 but variable motion  in space1 
excepting those of ,venus1 which are    
retrograde2 and the lines  of the nodes 
move with a variable velocity in the    
contrary direction4  ,the motions of    
both are extremely slow2 it requires    
more than #ajiggj  years for the major  
axis of the earth's orbit to accomplish 
a sidereal  revolution1 and #bjice years
 to complete its tropical motion4 ,the  
major  axis of ,jupiter's orbit requires
 no less than #aigefa years to perform  
its revolution from the disturbing      
action of ,saturn alone4 ,the periods   
in which the nodes revolve are also very
 great4 ,beside these1 the  inclination 
and eccentricity of every orbit are in a
 state of perpetual1  but slow change4  
,at the present time1 the inclinations  
of all the orbits  are decreasing2 but  

so slowly1 that the inclination of      
,jupiter's orbit  is only six minutes   
less now than it was in the age of      
,ptolemy4 ,the  terrestrial eccentricity
 is decreasing at the rate of #ciad     
miles in a  century2 and if it were to  
decrease equably1 it would be #cfcjj    
years  before the earth's orbit became a
 circle4 ,but in the midst of all these 
vicissitudes1 the major axes and mean   
motions of the planets remain           
permanently independent of secular      
changes2 they are so connected by       
,kepler's law of the squares of the     
periodic times being proportional to    
the cubes of the mean distances of the  
planets from the sun1 that one  cannot  
vary without affecting the other4       
,with the exception of these two        
elements1 it appears1 that all the      
bodies are in motion1 and every orbit is
 in a state of perpetual change4        
,minute as these changes are1 they might
 be supposed liable to accumulate  in   
the course of ages sufficiently to      

derange the whole order of nature1  to  
alter the relative positions of the     
planets1 to put an end to the           
vicissitudes of the seasons1 and to     
bring about collisions1 which would     
involve our whole system1 now so        
harmonious1 in chaotic confusion4 ,the  
consequences being so dreadful1 it is   
natural to inquire1 what proof  exists  
that creation will be preserved from    
such a catastrophe8 ,for  nothing can be
 known from observation1 since the      
existence of the human  race has        
occupied but a point in duration1 while 
these vicissitudes  embrace myriads of  
ages4 ,the proof is simple and          
convincing4 ,all the  variations of the 
solar system1 as well secular as        
periodic1 are  expressed analytically by
 the sines and cosines of circular arcs1
 which  increase with the time2 and as a
 sine or cosine never can exceed the    
radius1 but must oscillate between zero 
and unity1 however much the time  may   
increase1 it follows1 that when the     

variations have by slow changes         
accumulated in however long a time to a 
maximum1 they decrease by the  same slow
 degrees1 till they arrive at their     
smallest value1 and then  begin a new   
course1 thus for ever oscillating about 
a mean value4 ,this1  however1 would not
 be the case if the planets moved in a  
resisting  medium1 for then both the    
eccentricity and the major axes of the  
orbits  would vary with the time1 so    
that the stability of the system would  
be  ultimately destroyed4 ,but if the   
planets do move in an ethereal medium1  
it must be of extreme rarity1 since its 
resistance has hitherto been  quite     
insensible4    ,three circumstances have
 generally been supposed necessary to   
prove the  stability of the system3 the 
small eccentricities of the planetary   
orbits1 their small inclinations1 and   
the revolution of all the bodies1  as   
well planets as satellites1 in the same 
direction4 ,these1 however1  are not    
necessary conditions3 the periodicity of

 the terms in which the  inequalities   
are expressed is sufficient to assure   
us1 that though we do  not know the     
extent of the limits1 nor the period of 
that grand cycle  which probably        
embraces millions of years1 yet they    
never will exceed  what is requisite for
 the stability and harmony of the whole1
 for the  preservation of which every   
circumstance is so beautifully and      
wonderfully adapted4    ,the plane of   
the ecliptic itself1 though assumed to  
be fixed at a given  epoch for the      
convenience of astronomical computation1
 is subject to a  minute secular        
variation of #ebaji1 occasioned by the  
reciprocal action  of the planets2 but  
as this is also periodical1 the         
terrestrial equator1  which is inclined 
to it at an angle of about #bc #bh'1    
will never  coincide with the plane of  
the ecliptic2 so there never can be     
perpetual  spring4    ,the rotation of  
the earth is uniform2 therefore day and 
night1 summer  and winter1 will continue

 their vicissitudes while the system    
endures1  or is untroubled by foreign   
causes4                         ,yonder 
starry sphere       ,of planets1 and of 
fix'd1 in all her wheels                
,resembles nearest1 mazes intricate1    
,eccentric1 intervolv'd1 yet regular    
,then most1 when most irregular they    
seem4      ,the stability of our system 
was established by ,la ,grange1 'a      
discovery1'  says ,professor ,playfair1 
'that must render the name for ever     
memorable  in science1 and revered by   
those who delight in the contemplation  
of  whatever is excellent and sublime4  
,after ,newton's discovery of the       
elliptical orbits of the planets1 ,la   
,grange's discovery of their  periodical
 inequalities is without doubt the      
noblest truth in physical  astronomy2   
and1 in respect of the doctrine of final
 causes1 it may be  regarded as the     
greatest of all4'    ,notwithstanding   
the permanency of our system1 the       
secular variations in  the planetary    

orbits would have been extremely        
embarrassing to  astronomers1 when it   
became necessary to compare observations
 separated  by long periods4 ,this      
difficulty is obviated by ,la ,place1   
who has shown  that whatever changes    
time may induce either in the orbits    
themselves1  or in the plane of the     
ecliptic1 there exists an invariable    
plane  passing through the centre of    
gravity of the sun1 about which the     
whole  system oscillates within narrow  
limits1 and which is determined by this 
property2 that if every body in the     
system be projected on it1 and if  the  
mass of each be multiplied by the area  
described in a given time by  its       
projection on this plane1 the sum of all
 these products will be a  maximum4     
,this plane of greatest inertia1 by no  
means peculiar to the  solar system1 but
 existing in every system of bodies     
submitted to their  mutual attractions  
only1 always remains parallel to itself1
 and  maintains a fixed position1 whence

 the oscillations of the system may be  
estimated through unlimited time4 ,it is
 situate nearly half way between  the   
orbits of ,jupiter and ,saturn1 and is  
inclined to the ecliptic at an  angle of
 about #a #ce' #ca4    ,all the periodic
 and secular inequalities deduced from  
the law of  gravitation are so perfectly
 confirmed by observations1 that        
analysis  has become one of the most    
certain means of discovering the        
planetary  irregularities1 either when  
they are too small1 or too long in their
  periods1 to be detected by other      
methods4 ,jupiter and ,saturn1 however1 
exhibit inequalities which for a long   
time seemed discordant with that  law4  
,all observations1 from those of the    
,chinese and ,arabs down to the  present
 day1 prove that for ages the mean      
motions of ,jupiter and ,saturn  have   
been affected by great inequalities of  
very long periods1 forming  what        
appeared an anomaly in the theory of the
 planets4 ,it was long known  by        

observation1 that five times the mean   
motion of ,saturn is nearly  equal to   
twice that of ,jupiter2 a relation which
 the sagacity of ,la  ,place perceived  
to be the cause of a periodic inequality
 in the mean  motion of each of these   
planets1 which completes its period in  
nearly  #ibi ,julian years1 the one     
being retarded1 while the other is      
accelerated4 ,these inequalities are    
strictly periodical1 since they  depend 
on the configuration of the two planets2
 and the theory is  perfectly confirmed 
by observation1 which shows that in the 
course of  twenty centuries1 ,jupiter's 
mean motion has been accelerated by #c  
#bc'1  and ,saturn's retarded by #e     
#ac'4    ,it might be imagined that the 
reciprocal action of such planets as    
have  satellites would be different from
 the influence of those that have  none2
 but the distances of the satellites    
from their primaries are  incomparably  
less than the distances of the planets  
from the sun1 and  from one another1 so 

that the system of a planet and its     
satellites  moves nearly as if all those
 bodies were united in their common     
centre  of gravity2 the action of the   
sun however disturbs in some degree the 
motion of the satellites about their    
primary4    ,the changes that take place
 in the planetary system are exhibited  
on a  small scale by ,jupiter and his   
satellites2 and as the period requisite 
for the development of the inequalities 
of these little moons only  extends to a
 few centuries1 it may be regarded as an
 epitome of that  grand cycle which will
 not be accomplished by the planets in  
myriads of  centuries4 ,the revolutions 
of the satellites about ,jupiter are    
precisely  similar to those of the      
planets about the sun2 it is true they  
are  disturbed by the sun1 but his      
distance is so great1 that their motions
  are nearly the same as if they were   
not under his influence4 ,the           
satellites like the planets1 were       
probably projected in elliptical        

orbits1 but the compression of          
,jupiter's spheroid is very great in    
consequence of his rapid rotation2 and  
as the masses of the satellites  are    
nearly #ajjjjj times less than that of  
,jupiter1 the immense quantity  of      
prominent matter at his equator must    
soon have given the circular  form      
observed in the orbits of the first and 
second satellites1 which  its superior  
attraction will always maintain4 ,the   
third and fourth  satellites being      
further removed from its influence1 move
 in orbits with  a very small           
eccentricity4 ,the same cause occasions 
the orbits of the  satellites to remain 
nearly in the plane of ,jupiter's       
equator1 on  account of which they are  
always seen nearly in the same line2 and
 the  powerful action of that quantity  
of prominent matter is the reason why   
the motion of the nodes of these little 
bodies is so much more rapid  than those
 of the planet4 ,the nodes of the fourth
 satellite accomplish a  revolution in  

#ebj years1 while those of ,jupiter's   
orbit require no less  than #ejfgc      
years1 a proof of the reciprocal        
attraction between each  particle of    
,jupiter's equator and of the           
satellites4 ,although the two  first    
satellites sensibly move in circles1    
they acquire a small  ellipticity from  
the disturbances they experience4       
,the orbits of the satellites do not    
retain a permanent inclination1  either 
to the plane of ,jupiter's equator1 or  
to that of his orbit1 but  to certain   
planes passing between the two1 and     
through their  intersection2 these have 
a greater inclination to his equator the
  further the satellite is removed1 a   
circumstance entirely owing to the      
influence of ,jupiter's compression4    
,a singular law obtains among the mean  
motions and mean longitudes of the      
three first satellites4 ,it appears from
 observation1 that the mean  motion of  
the first satellite1 plus twice that of 
the third1 is equal to  three times that

 of the second1 and that the mean       
longitude of the first  satellite1 minus
 three times that of the second1 plus   
twice that of the  third1 is always     
equal to two right angles4 ,it is proved
 by theory1 that  if these relations had
 only been approximate when the         
satellites were  first launched into    
space1 their mutual attractions would   
have  established and maintained them4  
,they extend to the synodic motions of  
the satellites1 consequently they affect
 their eclipses1 and have a very  great 
influence on their whole theory4 ,the   
satellites move so nearly in  the plane 
of ,jupiter's equator1 which has a very 
small inclination to  his orbit1 that   
they are frequently eclipsed by the     
planet4 ,the instant  of the beginning  
or end of an eclipse of a satellite     
marks the same  instant of absolute time
 to all the inhabitants of the earth2   
therefore  the time of these eclipses   
observed by a traveller1 when compared  
with  the time of the eclipse computed  

for ,greenwich or any other fixed       
meridian1 gives the difference of the   
meridians in time1 and  consequently the
 longitude of the place of observation4 
,it has required  all the refinements of
 modern instruments to render the       
eclipses of  these remote moons         
available to the mariner2 now however1  
that system of  bodies invisible to the 
naked eye1 known to man by the aid of   
science  alone1 enables him to traverse 
the ocean1 spreading the light of       
knowledge and the blessings of          
civilization over the most remote       
regions1 and to return loaded with the  
productions of another  hemisphere4 ,nor
 is this all3 the eclipses of ,jupiter's
 satellites have  been the means or a   
discovery1 which1 though not so         
immediately  applicable to the wants of 
man1 unfolds a property of light1 that  
medium1 without whose cheering influence
 all the beauties of the  creation would
 have been to us a blank4 ,it is        
observed1 that those  eclipses of the   

first satellite which happen when       
,jupiter is near  conjunction1 are later
 by #af' #bf than those which take place
 when the  planet is in opposition4 ,but
 as ,jupiter is nearer to us when in    
opposition by the whole breadth of the  
earth's orbit than when in  conjunction1
 this circumstance was attributed to the
 time employed by  the rays of light in 
crossing the earth's orbit1 a distance  
of #aib  millions of miles2 whence it is
 estimated1 that light travels at the   
rate of #aibjjj miles in one second4    
,such is its velocity1 that the  earth1 
moving at the rate of nineteen miles in 
a second1 would take two  months to pass
 through a distance which a ray of light
 would dart over  in eight minutes4 ,the
 subsequent discovery of the aberration 
of light  confirmed this astonishing    
result4    ,objects appear to be situate
 in the direction of the rays that      
proceed  from them4 ,were light         
propagated instantaneously1 every       
object1 whether  at rest or in motion1  

would appear in the direction of these  
rays2 but  as light takes some time to  
travel1 when ,jupiter is in conjunction1
 we  see him by means of rays that left 
him #af' #bf before2 but during that    
time we have changed our position1 in   
consequence of the motion of the  earth 
in its orbit2 we therefore refer        
,jupiter to a place in which he is  not4
 ,his true position is in the diagonal  
of the parallelogram1 whose  sides are  
in the ratio of the velocity of light to
 the velocity of the  earth in its      
orbit1 which is as #aibjjj to #ai4 ,in  
consequence of  aberration1 none of the 
heavenly bodies are in the place in     
which they  seem to be4 ,in fact1 if the
 earth were at rest1 rays from a star   
would  pass along the axis of a         
telescope directed to it2 but if the    
earth were  to begin to move in its     
orbit with its usual velocity1 these    
rays would  strike against the side of  
the tube2 it would therefore be         
necessary to  incline the telescope a   

little1 in order to see the star4 ,the  
angle  contained between the axis of the
 telescope and a line drawn to the true 
place of the star1 is its aberration1   
which varies in quantity and  direction 
in different parts of the earth's orbit2
 but as it never  exceeds twenty        
seconds1 in ordinary cases4    ,the     
velocity of light deduced from the      
observed aberration of the fixed  stars1
 perfectly corresponds with that given  
by the eclipses of the  first satellite4
 ,the same result obtained from sources 
so different1  leaves not a doubt of its
 truth4 ,many such beautiful            
coincidences1  derived from apparently  
the most unpromising and dissimilar     
circumstances1 occur in physical        
astronomy1 and prove dependences which  
we might otherwise be unable to trace4  
,the identity of the velocity of  light 
at the distance of ,jupiter and on the  
earth's surface shows that  its velocity
 is uniform2 and if light consists in   
the vibrations of an  elastic fluid or  

ether filling space1 which hypothesis   
accords best with  observed phenomena1  
the uniformity of its velocity shows    
that the  density of the fluid          
throughout the whole extent of the solar
 system1  must be proportional to its   
elasticity4 ,among the fortunate        
conjectures  which have been confirmed  
by subsequent experience1 that of ,bacon
 is not  the least remarkable4 ,it      
produces in me1 says the restorer of    
true  philosophy1 a doubt1 whether the  
face of the serene and starry heavens   
be seen at the instant it really exists1
 or not till some time later2  and      
whether there be not1 with respect to   
the heavenly bodies1 a true  time and an
 apparent time1 no less than a true     
place and an apparent  place1 as        
astronomers say1 on account of parallax4
 ,for it seems  incredible that the     
species or rays of the celestial bodies 
can pass  through the immense interval  
between them and us in an instant2 or   
that  they do not even require some     

considerable portion of time4    ,as    
great discoveries generally lead to a   
variety of conclusions1 the  aberration 
of light affords a direct proof of the  
motion of the earth in  its orbit2 and  
its rotation is proved by the theory of 
falling bodies1  since the centrifugal  
force it induces retards the            
oscillations of the  pendulum in going  
from the pole to the equator4 ,thus a   
high degree of  scientific knowledge has
 been requisite to dispel the errors of 
the  senses4    ,the little that is     
known of the theories of the satellites 
of ,saturn and  ,uranus is in all       
respects similar to that of ,jupiter4   
,the great  compression of ,saturn      
occasions its satellites to move nearly 
in the  plane of its equator4 ,of the   
situation of the equator of ,uranus we  
know  nothing1 nor of its compression4  
,the orbits of its satellites are nearly
  perpendicular to the plane of the     
ecliptic4    ,our constant companion the
 moon next claims attention4 ,several   

circumstances concur to render her      
motions the most interesting1 and at    
the same time the most difficult to     
investigate of all the bodies of our    
system4 ,in the solar system planet     
troubles planet1 but in the lunar       
theory the sun is the great disturbing  
cause2 his vast distance being          
compensated by his enormous magnitude1  
so that the motions of the moon  are    
more irregular than those of the        
planets2 and on account of the  great   
ellipticity of her orbit and the size of
 the sun1 the  approximations to her    
motions are tedious and difficult1      
beyond what  those unaccustomed to such 
investigations could imagine4 ,neither  
the  eccentricity of the lunar orbit1   
nor its inclination to the plane of the 
ecliptic1 have experienced any changes  
from secular inequalities2 but  the mean
 motion1 the nodes1 and the perigee1 are
 subject to very  remarkable variations4
    ,from an eclipse observed at        
,babylon by the ,chaldeans1 on the #aith

 of  ,march1 seven hundred and          
twenty-one years before the ,christian  
era1 the  place of the moon is known    
from that of the sun at the instant of  
opposition2 whence her mean longitude   
may be found2 but the comparison  of    
this mean longitude with another mean   
longitude1 computed back for  the       
instant of the eclipse from modern      
observations1 shows that the moon       
performs her revolution round the earth 
more rapidly and in a shorter  time now1
 than she did formerly2 and that the    
acceleration in her mean  motion has    
been increasing from age to age as the  
square of the time2  all the ancient and
 intermediate eclipses confirm this     
result4 ,as the  mean motions of the    
planets have no secular inequalities1   
this seemed to  be an unaccountable     
anomaly1 and it was at one time         
attributed to the  resistance of an     
ethereal medium pervading space2 at     
another to the  successive transmission 
of the gravitating force3 but as ,la    

,place proved  that neither of these    
causes1 even if they exist1 have any    
influence on  the motions of the lunar  
perigee or nodes1 they could not affect 
the  mean motion1 a variation in the    
latter from such a cause being          
inseparably connected with variations in
 the two former of these  elements4     
,that great mathematician1 however1 in  
studying the theory of  ,jupiter's      
satellites1 perceived that the secular  
variations in the  elements of          
,jupiter's orbit1 from the action of the
 planets1 occasion  corresponding       
changes in the motions of the           
satellites3 this led him to  suspect    
that the acceleration in the mean motion
 of the moon might be  connected with   
the secular variation in the            
eccentricity of the  terrestrial orbit2 
and analysis has proved that he assigned
 the true  cause4    ,if the            
eccentricity of the earth's orbit were  
invariable1 the moon would  be exposed  
to a variable disturbance from the      

action of the sun1 in  consequence of   
the earth's annual revolution2 but it   
would be periodic1  since it would be   
the same as often as the sun1 the earth1
 and the moon  returned to the same     
relative positions3 on account however  
of the slow  and incessant diminution in
 the eccentricity of the terrestrial    
orbit1  the revolution of our planet is 
performed at different distances from   
the sun every year4 ,the position of the
 moon with regard to the sun1  undergoes
 a corresponding change2 so that the    
mean action of the sun on  the moon     
varies from one century to another1 and 
occasions the secular  increase in the  
moon's velocity called the acceleration1
 a name which is  very appropriate in   
the present age1 and which will continue
 to be so  for a vast number of ages to 
come2 because1 as long as the earth's   
eccentricity diminishes1 the moon's mean
 motion will be accelerated2 but  when  
the eccentricity has passed its minimum 
and begins to increase1 the  mean motion

 will be retarded from age to age4 ,at  
present the secular  acceleration is    
about #aj1 but its effect on the moon's 
place increases  as the square of the   
time4 ,it is remarkable that the action 
of the  planets thus reflected by the   
sun to the moon1 is much more sensible  
than their direct action1 either on the 
earth or moon4 ,the secular  diminution 
in the eccentricity1 which has not      
altered the equation of  the centre of  
the sun by eight minutes since the      
earliest recorded  eclipses1 has        
produced a variation of #a #dh' in the  
moon's longitude1  and of #g #ab' in her
 mean anomaly4    ,the action of the sun
 occasions a rapid but variable motion  
in the nodes  and perigee of the lunar  
orbit2 the former1 though they recede   
during  the greater part of the moon's  
revolution1 and advance during the      
smaller1 perform their sidereal         
revolutions in #fgic;days4#dbab1 and the
  latter1 though its motion is sometimes
 retrograde and sometimes direct1  in   

#cbcb;days4#ehjg1 or a little more than 
nine years3 but such is the  difference 
between the disturbing energy of the sun
 and that of all the  planets put       
together1 that it requires no less than 
#ajiggj years for the  greater axis of  
the terrestrial orbit to do the same4   
,it is evident that  the same secular   
variation which changes the sun's       
distance from the  earth1 and occasions 
the acceleration in the moon's mean     
motion1 must  affect the motion of the  
nodes and perigee2 and it consequently  
appears1  from theory as well as        
observation1 that both these elements   
are subject  to a secular inequality1   
arising from the variation in the       
eccentricity  of the earth's orbit1     
which connects them with the            
acceleration2 so that  both are retarded
 when the mean motion is anticipated4   
,the secular  variations in these three 
elements are in the ratio of the numbers
 #c1  #j4gce1 and #a2 whence the three  
motions of the moon1 with regard to the 

sun1 to her perigee1 and to her nodes1  
are continually accelerated1 and  their 
secular equations are as the numbers #a1
 #d1 and #j4bfe1 or according  to the   
most recent investigations as #a1 #d1   
#fggf and #j4cia4 ,a comparison  of     
ancient eclipses observed by the ,arabs1
 ,greeks1 and ,chaldeans1  imperfect as 
they are1 with modern observations1     
perfectly confirms  these results of    
analysis4    ,future ages will develop  
these great inequalities1 which at some 
most  distant period will amount to many
 circumferences4 ,they are indeed       
periodic2 but who shall tell their      
period8 ,millions of years must elapse  
before that great cycle is accomplished2
 but 'such changes1 though rare  in     
time1 are frequent in eternity4'    ,the
 moon is so near1 that the excess of    
matter at the earth's equator  occasions
 periodic variations in her longitude   
and latitude2 and1 as the  cause must be
 proportional to the effect1 a          
comparison of these  inequalities1      

computed from theory1 with the same     
given by observation1  shows that the   
compression of the terrestrial spheroid1
 or the ratio of  the difference between
 the polar and equatorial diameter to   
the diameter  of the equator is         
#a_/cje4je4 ,it is proved analytically1 
that if a fluid  mass of homogeneous    
matter1 whose particles attract each    
other inversely  as the square of the   
distance1 were to revolve about an axis1
 as the  earth1 it would assume the form
 of a spheroid1 whose compression is    
#a_/bcj4 ,whence it appears1 that the   
earth is not homogeneous1 but decreases 
in density from its centre to its       
circumference4 ,thus the moon's eclipses
  show the earth to be round1 and her   
inequalities not only determine the     
form1 but the internal structure of our 
planet2 results of analysis which  could
 not have been anticipated4 ,similar    
inequalities in ,jupiter's  satellites  
prove that his mass is not homogeneous1 
and that his  compression is #a_/ach4   

,the motions of the moon have now become
 of more importance to the  navigator   
and geographer than those of any other  
body1 from the  precision with which the
 longitude is determined by the         
occultations of  stars and lunar        
distances4 ,the lunar theory is brought 
to such  perfection1 that the times of  
these phenomena1 observed under any     
meridian1 when compared with that       
computed for ,greenwich in the ,nautical
  ,almanack1 gives the longitude of the 
observer within a few miles4 ,the       
accuracy of that work is obviously of   
extreme importance to a maritime        
nation2 we have reason to hope that the 
new ,ephemeris1 now in  preparation1    
will be by far the most perfect work of 
the kind that ever  has been published4 
,from the lunar theory1 the mean        
distance of the sun from the earth1 and 
thence the whole dimensions of the solar
 system are known2 for the  forces which
 retain the earth and moon in their     
orbits1 are respectively  proportional  

to the radii vectores of the earth and  
moon1 each being  divided by the square 
of its periodic time2 and as the lunar  
theory  gives the ratio of the forces1  
the ratio of the distance of the sun and
  moon from the earth is obtained3      
whence it appears that the sun's        
distance from the earth is nearly #cif  
times greater than that of the  moon4   
,the method however of finding the      
absolute distances of the celestial     
bodies in miles1 is in fact the same    
with that employed in measuring         
distances of terrestrial objects4 ,from 
the extremities of a known base  the    
angles which the visual rays from the   
object form with it1 are  measured2     
their sum subtracted from two           
right-angles gives the angle  opposite  
the base2 therefore by trigonometry1 all
 the angles and sides  of the triangle  
may be computed2 consequently the       
distance of the object  is found4 ,the  
angle under which the base of the       
triangle is seen from  the object1 is   

the parallax of that object2 it         
evidently increases and  decreases with 
the distance2 therefore the base must be
 very great  indeed1 to be visible at   
all from the celestial bodies4 ,but the 
globe  itself whose dimensions are      
ascertained by actual admeasurement1    
furnishes a standard of measures1 with  
which we compare the distances1  masses1
 densities1 and volumes of the sun and  
planets4    ,the courses of the great   
rivers1 which are in general navigable  
to a  considerable extent1 prove that   
the curvature of the land differs but   
little from that of the ocean2 and as   
the heights of the mountains and        
continents are1 at any rate1 quite      
inconsiderable when compared with the   
magnitude of the earth1 its figure is   
understood to be determined by a        
surface at every point perpendicular to 
the direction of gravity1 or of  the    
plumb-line1 and is the same which the   
sea would have if it were  continued all
 round the earth beneath the continents4

 ,such is the figure  that has been     
measured in the following manner3--     
,a terrestrial meridian is a line       
passing through both poles1 all the     
points of which have contemporaneously  
the same noon4 ,were the lengths  and   
curvatures of different meridians known1
 the figure of the earth  might be      
determined2 but the length of one degree
 is sufficient to give  the figure of   
the earth1 if it be measured on         
different meridians1 and  in a variety  
of latitudes2 for if the earth were a   
sphere1 all degrees  would be of the    
same length1 but if not1 the lengths of 
the degrees will  be greatest where the 
curvature is least2 a comparison of the 
length of  the degrees in different     
parts of the earth's surface will       
therefore  determine its size and form4 
,an arc of the meridian may be measured 
by observing the latitude of its        
extreme points1 and then measuring the  
distance between them in feet or        
fathoms2 the distance thus determined on

 the surface of the earth1  divided by  
the degrees and parts of a degree       
contained in the difference  of the     
latitudes1 will give the exact length of
 one degree1 the  difference of the     
latitudes being the angle contained     
between the  verticals at the           
extremities of the arc4 ,this would be  
easily  accomplished were the distance  
unobstructed1 and on a level with the   
sea2 but on account of the innumerable  
obstacles on the surface of the  earth1 
it is necessary to connect the extreme  
points of the arc by a  series of       
triangles1 the sides and angles of which
 are either measured  or computed1 so   
that the length of the arc is           
ascertained with much  laborious        
computation4 ,in consequence of the     
inequalities of the  surface1 each      
triangle is in a different plane2 they  
must therefore be  reduced by           
computation to what they would have     
been1 had they been  measured on the    
surface of the sea2 and as the earth is 

spherical1 they  require a correction to
 reduce them from plane to spherical    
triangles4    ,arcs of the meridian have
 been measured in a variety of          
latitudes1 both  north and south1 as    
well as arcs perpendicular to the       
meridian4 ,from  these measurements it  
appears that the length of the degrees  
increase  from the equator to the poles1
 nearly as the square of the sine of the
  latitude2 consequently1 the convexity 
of the earth diminishes from the        
equator to the poles4 ,many             
discrepancies occur1 but the figure that
 most  nearly follows this law is an    
ellipsoid of revolution1 whose          
equatorial  radius is #cifb4f miles1 and
 the polar radius #cidi4g2 the          
difference1 or  #ab4i miles1 divided by 
the equatorial radius1 is #a_/cjhg1 or  
#a_/cji  nearly2 this fraction is called
 the compression of the earth1 because1 
according as it is greater or less1 the 
terrestrial ellipsoid is more  or less  
flattened at the poles2 it does not     

differ much from that given  by the     
lunar inequalities4 ,if we assume the   
earth to be a sphere1 the  length of a  
degree of the meridian is #fi #a_/bb    
,british miles2 therefore  #cfj degrees1
 or the whole circumference of the globe
 is #bdhef1 and the  diameter1 which is 
something less than a third of the      
circumference1 is  #giaf or #hjjj miles 
nearly4 ,eratosthenes1 who died #aid    
years before the  ,christian era1 was   
the first to give an approximate value  
of the earth's  circumference1 by the   
mensuration of an arc between           
,alexandria and ,syene4    ,but there is
 another method of finding the figure of
 the earth1 totally  independent of     
either of the preceding4 ,if the earth  
were a homogeneous  sphere without      
rotation1 its attraction on bodies at   
its surface would  be everywhere the    
same2 if it be elliptical1 the force of 
gravity  theoretically ought to         
increase1 from the equator to the pole  
as the  square of the sine of the       

latitude2 but for a spheroid in         
rotation1 by  the laws of mechanics the 
centrifugal force varies as the square  
of the  sine of the latitude from the   
equator where it is greatest1 to the    
pole  where it vanishes2 and as it tends
 to make bodies fly off the surface1  it
 diminishes the effects of gravity by a 
small quantity4 ,hence by  gravitation1 
which is the difference of these two    
forces1 the fall of  bodies ought to be 
accelerated in going from the equator to
 the poles1  proportionably to the      
square of the sine of the latitude2 and 
the weight  of the same body ought to   
increase in that ratio4 ,this is        
directly proved  by the oscillations of 
the pendulum2 for if the fall of bodies 
be  accelerated1 the oscillations will  
be more rapid2 and that they may  always
 be performed in the same time1 the     
length of the pendulum must  be altered4
 ,now1 by numerous and very careful     
experiments1 it is proved  that a       
pendulum1 which makes #hfdjj            

oscillations in a mean day at the       
equator1 will do the same at every point
 of the earth's surface1 if  its length 
be increased in going to the pole1 as   
the square of the  sine of the latitude4
 ,from the mean of these it appears that
 the  compression of the terrestrial    
spheroid is about #a_/cdb1 which does   
not  differ much from that given by the 
lunar inequalities1 and from the arcs   
of the meridian4 ,the near coincidence  
of these three values1 deduced  by      
methods so entirely independent of each 
other1 shows that the mutual  tendencies
 of the centres of the celestial bodies 
to one another1 and  the attraction of  
the earth for bodies at its surface1    
result from the  reciprocal attraction  
of all their particles4 ,another proof  
may be added2  the nutation of the      
earth's axis1 and the precession of the 
equinoxes1  are occasioned by the action
 of the sun and moon on the protuberant 
matter at the earth's equator2 and      
although these inequalities do not  give

 the absolute value of the terrestrial  
compression1 they show that  the        
fraction expressing it is comprised     
between the limits  #a_/bgi and #a_/egh4
    ,it might be expected that the same 
compression should result from each1  if
 the different methods of observation   
could be made without error4  ,this1    
however1 is not the case2 for such      
discrepancies are found both  in the    
degrees of the meridian and in the      
length of the pendulum1 as  show that   
the figure of the earth is very         
complicated2 but they are  so small when
 compared with the general results1 that
 they may be  disregarded4 ,the         
compression deduced from the mean of the
 whole1  appears to be about #a_/cbj2   
that given by the lunar theory has the  
advantage  of being independent of the  
irregularities at the earth's surface1  
and of local attractions4 ,the form and 
size of the earth being determined1  it 
furnishes a standard of measure with    
which the dimensions of the  solar      

system may be compared4    ,the parallax
 of a celestial body is the angle under 
which the radius  of the earth would be 
seen if viewed from the centre of that  
body2  it affords the means of          
ascertaining the distances of the sun1  
moon1  and planets4 ,suppose that1 when 
the moon is in the horizon at the       
instant of rising or setting1 lines were
 drawn from her centre to the  spectator
 and to the centre of the earth1 these  
would form a right-angled  triangle with
 the terrestrial radius1 which is of a  
known length2  and as the parallax or   
angle at the moon can be measured1 all  
the angles  and one side are given2     
whence the distance of the moon from the
 centre  of the earth may be computed4  
,the parallax of an object may be found1
  if two observers under the same       
meridian1 but at a very great distance  
from one another1 observe its zenith    
distances on the same day at the  time  
of its passage over the meridian4 ,by   
such contemporaneous  observations at   

the ,cape of ,good ,hope and at ,berlin1
 the mean horizontal  parallax of the   
moon was found to be #cdedb2 whence the 
mean distance  of the moon is about     
sixty times the mean terrestrial radius1
 or #bdjjjj  miles nearly4 ,since the   
parallax is equal to the radius of the  
earth  divided by the distance of the   
moon2 under the same parallel of        
latitude  it varies with the distance of
 the moon from the earth1 and proves the
  ellipticity of the lunar orbit2 and   
when the moon is at her mean  distance1 
it varies with the terrestrial radii1   
thus showing that the  earth is not a   
sphere4    ,although the method         
described is sufficiently accurate for  
finding the  parallax of an object so   
near as the moon1 it will not answer for
 the  sun which is so remote1 that the  
smallest error in observation would     
lead to a false result2 but by the      
transits of ,venus that difficulty  is  
obviated4 ,when that planet is in her   
nodes1 or within #a #a_/d of them1  that

 is1 in1 or nearly in the plane of the  
ecliptic1 she is occasionally  seen to  
pass over the sun like a block spot4 ,if
 we could imagine that  the sun and     
,venus had no parallax1 the line        
described by the planet on  his disc1   
and the duration of the transit1 would  
be the same to all  the inhabitants of  
the earth2 but as the sun is not so     
remote but that  the semidiameter of the
 earth has a sensible magnitude when    
viewed from  his centre1 the line       
described by the planet in its passage  
over his  disc appears to be nearer to  
his centre or farther from it1 according
  to the position of the observer2 ,so  
that the duration of the transit  varies
 with the different points of the       
earth's surface at which it is          
observed4 ,this difference of time1     
being entirely the effect of parallax1  
furnishes the means of computing it from
 the known motions of the earth  and    
,venus1 by the same method as for the   
eclipses of the sun4 ,in fact  the ratio

 of the distances of ,venus and the sun 
from the earth at the  time of the      
transit1 are known from the theory of   
their elliptical  motion2 consequently1 
the ratio of the parallaxes of these two
 bodies1  being inversely as their      
distances1 is given2 and as the transit 
gives  the difference of the parallaxes1
 that of the sun is obtained4 ,in #agfi1
  the parallax of the sun was determined
 by observations of a transit of  ,venus
 made at ,wardhus in ,lapland1 and at   
,otaheite in the ,south ,sea1  the      
latter observation being the object of  
,cook's first voyage4 ,the  transit     
lasted about six hours at ,otaheite1 and
 the difference in the  duration at     
these two stations was eight minutes2   
whence the sun's  parallax was found to 
be #hgb2 but by other considerations it 
has  subsequently been reduced to #hege2
 from which the mean distance of  the   
sun appears to be about #ieiifjjj1 or   
ninety-six millions of miles  nearly4   
,this is confirmed by an inequality in  

the motion of the moon1  which depends  
on the parallax of the sun1 and which   
when compared  with observation gives   
#hf for the sun's parallax4    ,the     
parallax of ,venus is determined by her 
transits1 that of ,mars  by direct      
observation4 ,the distances of these two
 planets from the  earth are therefore  
known in terrestrial radii2 consequently
 their  mean distances from the sun may 
be computed and as the ratios of the    
distances of the planets from the sun   
are known by ,kepler's law1  their      
absolute distances in miles are easily  
found4    ,far as the earth seems to be 
from the sun1 it is near to him when    
compared with ,uranus2 that planet is no
 less than #ahdc millions of  miles from
 the luminary that warms and enlivens   
the world2 to it1  situate on the verge 
of the system1 the sun must appear not  
much  larger than ,venus does to us4    
,the earth cannot even be visible as a  
telescopic object to a body so remote2  
yet man1 the inhabitant of the  earth1  

soars beyond the vast dimensions of the 
system to which his  planet belongs1 and
 assumes the diameter of its orbit as   
the base  of a triangle1 whose apex     
extends to the stars4    ,sublime as the
 idea is1 this assumption proves        
ineffectual1 for  the apparent places of
 the fixed stars are not sensibly       
changed by  the earth's annual          
revolution2 and with the aid derived    
from the  refinements of modern         
astronomy and the most perfect          
instruments1  it is still a matter of   
doubt whether a sensible parallax has   
been  detected1 even in the nearest of  
these remote suns4 ,if a fixed star  had
 the parallax of one second1 its        
distance from the sun would be          
#bjejjjjj millions of miles4 ,at such a 
distance not only the terrestrial  orbit
 shrinks to a point1 but1 where the     
whole solar system1 when  seen in the   
focus of the most powerful telescope1   
might be covered  by the thickness of a 
spider's thread4 ,light1 flying at the  

rate  of #bjjjjj miles in a second1     
would take three years and seven days   
to travel over that space2 one of the   
nearest stars may therefore  have been  
kindled or extinguished more than three 
years before we  could have been aware  
of so mighty an event4 ,but this        
distance must  be small when compared   
with that of the most remote of the     
bodies  which are visible in the        
heavens4 ,the fixed stars are           
undoubtedly  luminous like the sun2 it  
is therefore probable that they are not 
nearer to one another than the sun is to
 the nearest of them4 ,in  the milky way
 and the other starry nebul1 some of the
 stars that  seem to us to be close to  
others1 may be far behind them in the   
boundless depth of space2 nay1 may      
rationally be supposed to be  situated  
many thousand times further off3 light  
would therefore  require thousands of   
years to come to the earth from those   
myriads  of suns1 of which our own is   
but 'the dim and remote companion4'     

,the masses of such planets as have no  
satellites are known by comparing  the  
inequalities they produce in the motions
 of the earth and of each  other1       
determined theoretically1 with the same 
inequalities given by  observation1 for 
the disturbing cause must necessarily be
 proportional  to the effect it         
produces4 ,but as the quantities of     
matter in any two  primary planets are  
directly as the cubes of the mean       
distances at which  their satellites    
revolve1 and inversely as the squares of
 their periodic  times1 the mass of the 
sun and of any planets which have       
satellites1 may  be compared with the   
mass of the earth4 ,in this manner it is
 computed  that the mass of the sun is  
#cedicf times greater than that of the  
earth2  whence the great perturbations  
of the moon and the rapid motion of the 
perigee and nodes of her orbit4 ,even   
,jupiter1 the largest of the  planets1  
is #ajgj4e times less than the sun4 ,the
 mass of the moon is  determined from   

four different sources1--from her action
 on the  terrestrial equator1 which     
occasions the rotation in the axis of   
rotation2 from her horizontal parallax1 
from an inequality she produces  in the 
sun's longitude1 and from her action on 
the titles4 ,the three  first           
quantities1 computed from theory1 and   
compared with their observed  values1   
give her mass respectively equal to the 
#a_/ga1 #a_/gdb1 and #a_/fib  part of   
that of the earth1 which do not differ  
very much from each  other2 but1 from   
her action in raising  the tides1 which 
furnishes  the fourth method1 her mass  
appears to be about the seventy-fifth   
part  of that of the earth1 a value that
 cannot differ much from the truth4     
,the apparent diameters of the sun1     
moon1 and planets are determined by     
measurement2 therefore their real       
diameters may be compared with that of  
the earth2 for the real diameter of a   
planet is to the real diameter of  the  
earth1 or #hjjj miles1 as the apparent  

diameter of the planet to the  apparent 
diameter of the earth as seen from the  
planet1 that is1 to  twice the parallax 
of the planet ,the mean apparent        
diameter of the sun  is #aibj1 and with 
the solar parallax #hfe1 it will be     
found that  the diameter of the sun is  
about #hhhjjj miles2 therefore1 the     
centre of  the sun were to coincide with
 the centre of the earth1 his volume    
would  not only include the orbit of the
 moon1 but would extend nearly as far   
again1 for the moon's mean distance from
 the earth is about sixty times  the    
earth's mean radius or #bdjjjj miles2 so
 that twice the distance of  the moon is
 #dhjjjj miles1 which differs but little
 from the solar  radius2 his equatorial 
radius is probably not much less than   
the major  axis of the lunar orbit4     
,the diameter of the moon is only #bafj 
miles2 and ,jupiter's diameter of       
#hhjjj miles is incomparably less than  
that of the sun ,the diameter of        
,pallas does not much exceed #ga miles1 

so that an inhabitant of that  planet1  
in one of our steam-carriages1 might go 
round his world in five  or six hours4  
,the oblate form of the celestial bodies
 indicates rotatory motion1 and  this   
has been confirmed1 in most cases1 by   
tracing spots on their  surfaces1 whence
 their poles and times of rotation have 
been determined4  ,the rotation of      
,mercury is unknown1 on account of his  
proximity to the  sun2 and that of the  
new planets has not yet been            
ascertained4 ,the sun  revolves in      
twenty-five days ten hours1 about an    
axis that is directed  towards a point  
half way between the pole star and      
,lyra1 the plane of  rotation being     
inclined a little more than #gj to that 
on which the  earth revolves4 ,from the 
rotation of the sun1 there is every     
reason to  believe that he has a        
progressive motion in space1 although   
the  direction to which he tends is as  
yet unknown2 but in consequence of the  
reaction of the planets1 he describes a 

small irregular orbit about the  centre 
of inertia of the system1 never         
deviating from his position by  more    
than twice his own diameter1 or about   
seven times the distance of  the moon   
from the earth4    ,the sun and all his 
attendants rotate from west to east on  
axes that  remain nearly parallel to    
themselves in every point of their      
orbit1 and  with angular velocities that
 are sensibly uniform4 ,although the    
uniformity in the direction of their    
rotation is a circumstance hitherto     
unaccounted for in the economy of       
,nature1 yet from the design and        
adaptation of every other part to the   
perfection of the whole1 a  coincidence 
so remarkable cannot be accidental2 and 
as the revolutions  of the planets and  
satellites are also from west to east1  
it is evident  that both must have      
arisen from the primitive causes which  
have  determined the planetary motions4 
,the larger planets rotate in shorter   
periods than the smaller planets  and   

the earth2 their compression is         
consequently greater1 and the action  of
 the sun and of their satellites        
occasions a nutation in their axes1  and
 a precession of their equinoxes1       
similar to that which obtains in  the   
terrestrial spheroid from the attraction
 of the sun and moon on the  prominent  
matter at the equator4 ,in comparing the
 periods of the  revolutions of ,jupiter
 and ,saturn with the times of their    
rotation1 it  appears that a year of    
,jupiter contains nearly ten thousand of
 his days1  and that of ,saturn about   
thirty thousand ,saturnian days4    ,the
 appearance of ,saturn is unparalleled  
in the system of the world2 he  is      
surrounded by a ring even brighter than 
himself1 which always remains  in the   
plane of his equator1 and viewed with a 
very good telescope1 it  is found to    
consist of two concentric rings1 divided
 by a dark band4 ,by  the laws of       
mechanics1 it is impossible that this   
body can retain its  position by the    

adhesion of its particles alone2 it must
 necessarily  revolve with a velocity   
that will generate a centrifugal force  
sufficient to balance the attraction of 
,saturn4 ,observation confirms the      
truth of these principles1 showing that 
the rings rotate about the  planet in   
#aj #a_/b hours1 which is considerably  
less than the time a  satellite would   
take to revolve about ,saturn at the    
same distance4 ,their  plane is inclined
 to the ecliptic at an angle of #ca2 and
 in consequence  of this obliquity of   
position they always appear elliptical  
to us1 but  with an eccentricity so     
variable as even to be occasionally like
 a  straight line drawn across the      
planet4 ,at present the apparent axes of
  the rings are as #ajjj to #afj2 and on
 the #bith of ,september1 #ahcb1  the   
plane of the rings will pass through the
 centre of the earth  when they will be 
visible only with superior instruments1 
and will  appear like a fine line across
 the disc of ,saturn4 ,on the #ast of   

,december in the same year1 the plane of
 the rings will pass through  the centre
 of the sun4    ,it is a singular result
 of the theory1 that the rings could not
 maintain  their stability of rotation  
if they were everywhere of uniform      
thickness2 for the smallest disturbance 
would destroy the equilibrium1  which   
would become more and more deranged1    
till at last they would be  precipitated
 on the surface of the planet4 ,the     
rings of ,saturn must  therefore be     
irregular solids of unequal breadth in  
the different parts  of the             
circumference1 so that their centres of 
gravity do not coincide  with the       
centres of their figures4    ,professor 
,struve has also discovered that the    
centre of the ring is not  concentric   
with the centre of ,saturn2 the interval
 between the outer  edge of the globe of
 the planet and the outer edge of the   
ring on one  side1 is #aajgc1 and on the
 other side the interval is #aabhh2     
consequently there is an eccentricity of

 the globe in the ring of  #jbae4    ,if
 the rings obeyed different forces1 they
 would not remain in the same  plane1   
but the powerful attraction of ,saturn  
always maintains them and  his          
satellites in the plane of his equator4 
,the rings1 by their mutual  action1 and
 that of the sun and satellites1 must   
oscillate about the  centre of ,saturn1 
and produce phenomena of light and      
shadow1 whose  periods extend to many   
years4    ,the periods of the rotation  
of the moon and the other satellites are
  equal to the times of their           
revolutions1 consequently these bodies  
always turn the same face to their      
primaries2 however1 as the mean  motion 
of the moon is subject to a secular     
inequality which will  ultimately amount
 to many circumferences1 if the rotation
 of the moon  were perfectly uniform1   
and not affected by the same            
inequalities1 it  would cease exactly to
 counterbalance the motion of           
revolution2 and the  moon1 in the course

 of ages1 would successively and        
gradually discover  every point other   
surface to the earth4 ,but theory proves
 that this  never can happen2 for the   
rotation of the moon1 though it does not
  partake of the periodic inequalities  
of her revolution1 is affected by  the  
same secular variations1 so that her    
motions of rotation and  revolution     
round the earth will always balance each
 other1 and remain  equal4 ,this        
circumstance arises from the form of the
 lunar spheroid1  which has three       
principal axes of different lengths at  
right angles to  each other4 ,the moon  
is flattened at the poles from her      
centrifugal  force1 therefore her polar 
axis is least2 the other two are in the 
plane  of her equator1 but that directed
 towards the earth is the greatest4 ,the
  attraction of the earth1 as if it had 
drawn out that part of the moon's       
equator1 constantly brings the greatest 
axis1 and consequently the same         
hemisphere towards us1 which makes her  

rotation participate in the  secular    
variations in her mean motion of        
revolution4 ,even if the angular        
velocities of rotation and revolution   
had not been nicely balanced in  the    
beginning of the moon's motion1 the     
attraction of the earth would  have     
recalled the greatest axis to the       
direction of the line joining the       
centres of the earth and moon2 so that  
it would vibrate on each side of  that  
line in the same manner as a pendulum   
oscillates on each side of  the vertical
 from the influence of gravitation4     
,no such libration is perceptible2 and  
as the smallest disturbance would  make 
it evident1 it is clear that if the moon
 has ever been touched by a  comet1 the 
mass of the latter must have been       
extremely small2 for if it  had been    
only the hundred-thousandth part of that
 of the earthy it would  have rendered  
the libration sensible4 ,a similar      
libration exists in the  motions of     
,jupiter's satellites2 but although the 

comet of #agfg and #aggi  passed through
 the midst of them1 their libration     
still remains  insensible4 ,it is true1 
the moon is liable to librations        
depending on  the position of the       
spectator2 at her rising1 part of the   
western edge  of her disc is visible1   
which is invisible at her setting1 and  
the  contrary takes place with regard to
 her eastern edge4 ,there are also      
librations arising from the relative    
positions of the earth and moon in      
their respective orbits1 but as they are
 only optical appearances1 one          
hemisphere will be eternally concealed  
from the earth4 ,for the same  reason1  
the earth1 which must be so splendid an 
object to one lunar  hemisphere1 will be
 for ever veiled from the other4 ,on    
account of these  circumstances1 the    
remoter hemisphere of the moon has its  
day a  fortnight long1 and a night of   
the same duration not even enlightened  
by  a moon1 while the favoured side is  
illuminated by the reflection of the    

earth during its long night4 ,a moon    
exhibiting a surface thirteen times     
larger than ours1 with all the varieties
 of clouds1 land1 and water  coming     
successively into view1 would be a      
splendid object to a lunar  traveller in
 a journey to his antipodes4    ,the    
great height of the lunar mountains     
probably has a considerable  influence  
on the phenomena of her motion1 the more
 so as her compression  is small1 and   
her mass considerable4    ,in the curve 
passing through the poles1 and that     
diameter of the moon  which always      
points to the earth1 nature has         
furnished a permanent  meridian1 to     
which the different spots on her surface
 have been  referred1 and their         
positions determined with as much       
accuracy as those  of many of the most  
remarkable places on the surface of our 
globe4    ,the rotation of the earth    
which determines the length of the day  
may be  regarded as one of the most     
important elements in the system of the 

world4 ,it serves as a measure of time1 
and forms the standard of  comparison   
for the revolutions of the celestial    
bodies1 which by their  proportional    
increase or decrease would soon disclose
 any changes it  might sustain4 ,theory 
and observation concur in proving1 that 
among the  innumerable vicissitudes that
 prevail throughout creation1 the period
 of  the earth's diurnal rotation is    
immutable4 ,a fluid1 as ,mr4 ,babbage   
observes1 in falling from a higher to a 
lower level1 carries with it the        
velocity due to its revolution with the 
earth at a greater distance from  its   
centre4 ,it will therefore accelerate1  
although to an almost  infinitesimal    
extent1 the earth's daily rotation4 ,the
 sum of all these  increments of        
velocity1 arising from the descent of   
all the rivers on  the earth's surface1 
would in time become perceptible1 did   
not nature1  by the process of          
evaporation1 raise the waters back to   
their sources2  and thus again by       

removing matter to a greater distance   
from the centre1  destroy the velocity  
generated by its previous approach2 so  
that the  descent of the rivers does not
 affect the earth's rotation4 ,enormous 
masses projected by volcanoes from the  
equator to the poles1 and the  contrary1
 would indeed affect it1 but there is no
 evidence of such  convulsions4 ,the    
disturbing action of the moon and       
planets1 which has so  powerful an      
effect on the revolution of the earth1  
in no way influences  its rotation3 the 
constant friction of the trade winds on 
the mountains  and continents between   
the tropics does not impede its         
velocity1 which  theory even proves to  
be the same1 as if the sea together with
 the earth  formed one solid mass4 ,but 
although these circumstances be         
inefficient1  a variation in the mean   
temperature would certainly occasion a  
corresponding change in the velocity of 
rotation3 for in the science of         
dynamics1 it is a principle in a system 

of bodies1 or of particles  revolving   
about a fixed centre1 that the momentum1
 or sum of the  products of the mass of 
each into its angular velocity and      
distance from  the centre is a constant 
quantity1 if the system be not deranged 
by an  external cause4 ,now since the   
number of particles in the system is the
  same whatever its temperature may be1 
when their distances from the  centre   
are diminished1 their angular velocity  
must be increased in order  that the    
preceding quantity may still remain     
constant4 ,it follows then1  that as the
 primitive momentum of rotation with    
which the earth was  projected into     
space must necessarily remain the same1 
the smallest  decrease in heat1 by      
contracting the terrestrial spheroid1   
would  accelerate its rotation1 and     
consequently diminish the length of the 
day4 ,notwithstanding the constant      
accession of heat from the sun's rays1  
geologists have been induced to believe 
from the nature of fossil  remains1 that

 the mean temperature of the globe is   
decreasing4    ,the high temperature of 
mines1 hot springs1 and above all1 the  
internal  fires that have produced1 and 
do still occasion such devastation on   
our  planet1 indicate an augmentation of
 heat towards its centre the increase   
of density in the strata corresponding  
to the depth and the form of the        
spheroid1 being what theory assigns to a
 fluid mass in rotation1 concur  to     
induce the idea that the temperature of 
the earth was originally so  high as to 
reduce all the substances of which it is
 composed to a state  of fusion1 and    
that in the course of ages it has cooled
 down to its  present state2 that it is 
still becoming colder1 and that it will 
continue to do so1 till the whole mass  
arrives at the temperature of the       
medium in which it is placed1 or rather 
at a state of equilibrium  between this 
temperature1 the cooling power of its   
own radiation1 and  the heating effect  
of the sun's rays4 ,but even if this    

cause be  sufficient to produce the     
observed effects1 it must be extremely  
slow in  its operation2 for in          
consequence of the rotation of the earth
 being a  measure of the periods of the 
celestial motions1 it has been proved1  
that if the length of the day had       
decreased by the three hundredth part   
of a second since the observations of   
,hipparchus two thousand years ago1  it 
would have diminished the secular       
equation of the moon by #dd4 ,it  is    
therefore beyond a doubt1 that the mean 
temperature of the earth  cannot have   
sensibly varied during that time2 if    
then the appearances  exhibited by the  
strata really owing to a decrease of    
internal  temperature1 it either shows  
the immense periods requisite to produce
  geological changes to which two       
thousand years are as nothing1 or that  
the mean temperature of the earth had   
arrived at a state of equilibrium       
before these observations4 ,however     
strong the indication of the  primitive 

fluidity of the earth1 as there is no   
direct proof1 it can  only be regarded  
as a very probable hypothesis2 but one  
of the most  profound philosophers and  
elegant writers of modern times has     
found1 in  the secular variation of the 
eccentricity of the terrestrial orbit1  
an  evident cause of decreasing         
temperature4 ,that accomplished author1 
in  pointing out the mutual dependences 
of phenomena1 says--',it is evident     
that the mean temperature of the whole  
surface of the globe1 in so far  as it  
is maintained by the action of the sun  
at #h higher degree than it  would have 
were the sun extinguished1 must depend  
on the mean quantity  of the sun's rays 
which it receives1 or1 which comes to   
the same thing1  on the total quantity  
received in a given invariable time3 and
 the  length of the year being          
unchangeable in all the fluctuations of 
the  planetary system1 it follows1 that 
the total amount of solar radiation     
will determine1 cteris paribus1 the     

general climate of the earth4 ,now  it  
is not difficult to show1 that this     
amount is inversely proportional  to the
 minor axis of the ellipse described by 
the earth about the sun1  regarded as   
slowly variable2 and that1 therefore1   
the major axis  remaining1 as we know it
 to be1 constant1 and the orbit being   
actually  in a state of approach to a   
circle1 and consequently the minor axis 
being on the increase1 the mean annual  
amount of solar radiation  received by  
the whole earth must be actually on the 
decrease4 ,we have1  therefore1 an      
evident real cause to account for the   
phenomenon4' ,the  limits of the        
variation in the eccentricity of the    
earth's orbit are  unknown2 but if its  
ellipticity has ever been as great as   
that of the  orbit of ,mercury or       
,pallas1 the mean temperature of the    
earth must have  been sensibly higher   
than it is at present2 whether it was   
great enough  to render our northern    
climates fit for the production of      

tropical  plants1 and for the residence 
of the elephant1 and the other          
inhabitants  of the torrid zone1 it is  
impossible to say4    ,the relative     
quantity of heat received by the earth  
at different moments  during a single   
revolution1 varies with the position of 
the perigee of  its orbit1 which        
accomplishes a tropical revolution in   
#bjice years4 ,in  the year #abej of our
 era1 and #bifec years before it1 the   
perigee  coincided with the summer      
solstice2 at both these periods the     
earth was  nearer the sun during the    
summer1 and farther from him in the     
winter  than in any other position of   
the apsides3 the extremes of temperature
  must therefore have been greater than 
at present2 but as the terrestrial      
orbit was probably more elliptical at   
the distant epoch1 the heat of the      
summers must have been very great though
 possibly compensated by the  rigour of 
the winters2 at all events1 none of     
these changes affect the  length of the 

day4    ,it appears from the marine     
shells found on the tops of the highest 
mountains1 and in almost every part of  
the globe1 that immense  continents have
 been elevated above the ocean1 which   
must have which  must have engulphed    
others4 ,such a catastrophe would be    
occasioned by a  variation in the       
position of the axis of rotation on the 
surface of the  earth2 for the seas     
ending to the new equator would leave   
some portions  of the globe1 and        
overwhelm others4    ,but theory proves 
that neither nutation1 precession1 nor  
any of the  disturbing forces that      
affect the system1 have the smallest    
influence on  the axis of rotation1     
which maintains a permanent position on 
the  surface1 if the earth be not       
disturbed in its rotation by some       
foreign  cause1 as the collision of a   
comet which may have happened in the    
immensity of time4 ,then indeed1 the    
equilibrium could only have been        
restored by the rushing of the seas to  

the new equator1 which they would       
continue to do1 till the surface was    
every where perpendicular to the        
direction of gravity4 ,but it is        
probable that such an accumulation of   
the waters would not be sufficient to   
restore equilibrium if the  derangement 
had been great2 for the mean density of 
the sea is only  about a fifth part of  
the mean density of the earth1 and the  
mean depth  even of the ,pacific ocean  
is not more than four miles1 whereas the
  equatorial radius of the earth exceeds
 the polar radius by twenty-five  or    
thirty miles2 consequently the influence
 of the sea on the direction  of gravity
 is very small2 and as it appears that a
 great change in the  position of the   
axes is incompatible with the law of    
equilibrium1 the  geological phenomena  
must be ascribed to an internal cause4  
,thus amidst  the mighty revolutions    
which have swept innumerable races of   
organized  beings from the earth1 which 
have elevated plains1 and buried        

mountains  in the ocean1 the rotation of
 the earth1 and the position of the axis
 on  its surface1 have undergone but    
slight variations4    ,it is beyond a   
doubt that the strata increase in       
density from the  surface of the earth  
to its centre1 which is even proved by  
the lunar  inequalities2 and it is      
manifest from the mensuration of arcs of
 the  meridian and the lengths of the   
seconds pendulum that the strata are    
elliptical and concentric4 ,this        
certainly would have happened if the    
earth had originally been fluid1 for the
 denser parts must have subsided        
towards the centre1 as it approached a  
state of equilibrium2 but the  enormous 
pressure of the superincumbent mass is a
 sufficient cause for  these phenomena4 
,professor ,leslie observes1 that air   
compressed into the  fiftieth part of   
its volume has its elasticity fifty     
times augmented2 if  it continue to     
contract at that rate1 it would1 from   
its own incumbent  weight1 acquire the  

density of water at the depth of        
thirty-four miles4  ,but water itself   
would have its density doubled at the   
depth of  ninety-three miles1 and would 
even attain the density of quicksilver  
at  a depth of #cfb miles4 ,in          
descending therefore towards the centre 
through  #djjj miles1 the condensation  
of ordinary materials would surpass the 
utmost powers of conception4 ,but a     
density so extreme is not borne out  by 
astronomical observation4 ,it might seem
 therefore to follow1 that our  planet  
must have a widely cavernous structure1 
and that we tread on a  crust or shell1 
whose thickness bears a very small      
proportion to the  diameter of its      
sphere4 ,possibly too this great        
condensation at the  central regions may
 be counterbalanced by the increased    
elasticity due  to a very elevated      
temperature4 ,dr4 ,young says that steel
 would be  compressed into one-fourth1  
and stone into one-eighth of its bulk at
 the  earth's centre4 ,however we are   

yet ignorant of the laws of compression 
of solid bodies beyond a certain limit2 
but1 from the experiments of ,mr4       
,perkins1 they appear to be capable of a
 greater degree of compression  than has
 generally been imagined4    ,it appears
 then1 that the axis of rotation is     
invariable on the surface  of the earth1
 and observation shows1 that were it not
 for the action of  the sun and moon on 
the matter at the equator1 it would     
remain parallel  to itself in every     
point of its orbit4    ,the attraction  
of an exterior body not only draws a    
spheroid towards it2  but1 as the force 
varies inversely as the square of the   
distance1 it  gives it a motion about   
its centre of gravity1 unless when the  
attracting body is situated in the      
prolongation of one of the axes of  the 
spheroid4    ,the plane of the equator  
is inclined to the plane of the ecliptic
 at an  angle of about #bc #bh'1 and the
 inclination of the lunar orbit on the  
same is nearly #e2 consequently1 from   

the oblate figure of the earth1  the sun
 and moon acting obliquely and unequally
 on the different parts  of the         
terrestrial spheroid1 urge the plane of 
the equator from its  direction1 and    
force it to move from east to west1 so  
that the  equinoctial points have a slow
 retrograde motion on the plane of the  
ecliptic of about #ejdab annually4 ,the 
direct tendency of this action  would be
 to make the planes of the equator and  
ecliptic coincide2 but in  consequence  
of the rotation of the earth1 the       
inclination of the two  planes remains  
constant1 as a top in spinning preserves
 the same  inclination to the plane of  
the horizon4 ,were the earth spherical  
this  effect would not be produced1 and 
the equinoxes would always correspond   
to the same points of the ecliptic1 at  
least as far as this kind of  action is 
concerned4 ,but another and totally     
different cause operates on  this       
motion1 which has already been          
mentioned4 ,the action of the planets   

on one another and on the sun1 occasions
 a very slow variation in the  position 
of the plane of the ecliptic1 which     
affects its inclination on  the plane of
 the equator1 and gives the equinoctial 
points a slow but  direct motion on the 
ecliptic of #jcab annually1 which is    
entirely  independent of the figure of  
the earth1 and would be the same if it  
were  a sphere4 ,thus the sun and moon1 
by moving the plane of the equator1     
cause the equinoctial points to         
retrograde on the ecliptic2 and the     
planets1 by moving the plane of the     
ecliptic1 give them a direct motion1    
but much less than the former2          
consequently the difference of the two  
is  the mean precession1 which is       
proved1 both by theory and observation1 
to  be about #eja annually4 ,as the     
longitudes of all the fixed stars are   
increased by this quantity1 the effects 
of precession are soon detected2  it was
 accordingly discovered by ,hipparchus1 
in the year #abh before  ,christ1 from a

 comparison of his own observations with
 those of  ,timocharis1 #aee years      
before4 ,in the time of ,hipparchus the 
entrance of  the sun into the           
constellation ,aries was the beginning  
of spring1 but  since then the          
equinoctial points have receded #cj2 so 
that the  constellations called the     
signs of the zodiac are now at a        
considerable  distance from those       
divisions of the ecliptic which bear    
their names4  ,moving at the rate of    
#eja annually1 the equinoctial points   
will  accomplish a revolution in #behfh 
years2 but as the precession varies in  
different centuries1 the extent of this 
period will be slightly  modified4      
,since the motion of the sun is direct1 
and that of the  equinoctial points     
retrograde1 he takes a shorter time to  
return to the  equator than to arrive at
 the same stars2 so that the tropical   
year of  #cfe4bdbbfd days must be       
increased by the time he takes to move  
through  an arc of #eja1 in order to    

have the length of the sidereal year4   
,by  simple proportion it is the        
#j4jadaaith part of a day1 so that the  
sidereal year is #cfe4befchc4    ,the   
mean annual precession is subject to a  
secular variation2 for  although the    
change in the plane of the ecliptic     
which is the orbit of  the sun1 be      
independent of the form of the earth1   
yet by bringing the  sun1 moon and earth
 into different relative positions from 
age to age1  it alters the direct action
 of the two first on the prominent      
matter at  the equator2 on this account 
the motion of the equinox is greater by 
#jdee now than it was in the lime of    
,hipparchus2 consequently the  actual   
length of the tropical year is about    
#daed shorter than it was  at that time4
 ,the utmost change that it can         
experience from this cause  amounts to  
#dc4    ,such is the secular motion of  
the equinoxes1 but it is sometimes      
increased and sometimes diminished by   
periodic variations1 whose periods      

depend on the relative positions of the 
sun and moon with regard to the  earth1 
and occasioned by the direct action of  
these bodies on the  equator4 ,dr4      
,bradley discovered that by this action 
the moon causes the  pole of the equator
 to describe a small ellipse in the     
heavens1 the  diameters of which are #af
 and #bj4 ,the period of this inequality
 is  nineteen years1 the time employed  
by the nodes of the lunar orbit to      
accomplish a revolution4 ,the sun causes
 a small variation in the  description  
of this ellipse2 it runs through its    
period in half a year4  ,this nutation  
in the earth's axis affects both the    
precession and  obliquity with small    
periodic variations2 but in consequence 
of the  secular variation in the        
position of the terrestrial orbit1 which
 is  chiefly owing to the disturbing    
energy of ,jupiter on the earth1 the    
oblique of the ecliptic is annually     
diminished by #jebaji4 ,with  regard to 
the fixed stars1 this variation in the  

course of ages may  amount to tea or    
eleven degrees2 but the obliquity of the
 ecliptic to  the equator can never vary
 more than two or three degrees1 since  
the  equator will follow in some measure
 the motion of the ecliptic4    ,it is  
evident that the places of all the      
celestial bodies are affected  by       
precession and nutation1 and therefore  
all observations of them must  be       
corrected for these inequalities4       
,the densities of bodies are            
proportional to their masses divided by 
their volumes2 hence if the sun and     
planets be assumed to be spheres1  their
 volumes will be as the cubes of their  
diameters4 ,now the apparent  diameters 
of the sun and earth at their mean      
distance1 are #aibb and  #agjh1 and the 
mass of the earth is the #a_/cedicfth   
part of that of the  sun taken as the   
unit2 it follows therefore1 that the    
earth is nearly  four times as dense as 
the sun2 but the sun is so large that   
his  attractive force would cause bodies

 to fall through about #dej feet  in a  
second2 consequently if he were even    
habitable by human beings1  they would  
be unable to move1 since their weight   
would be thirty  times as great as it is
 here4 ,a moderate sized man would weigh
 about  two tons at the surface of the  
sun4 ,on the contrary1 at the surface   
of the four new planets we should be so 
light1 that it would be  impossible to  
stand from the excess of our muscular   
force1 for a man  would only weigh a few
 pounds4 ,all the planets and satellites
 appear  to be of less density than the 
earth4 ,the motions of ,jupiter's       
satellites show that his density        
increases towards his centre2 and  the  
singular irregularities in the form of  
,saturn1 and the great  compression of  
,mars1 prove the internal structure of  
these two planets  to be very far from  
uniform4    ,astronomy has been of      
immediate and essential use in affording
  invariable standards for measuring    
duration1 distance1 magnitude1 and      

velocity4 ,the sidereal day1 measured by
 the time elapsed between two           
consecutive transits of any star at the 
same meridian1 and the sidereal  year1  
are immutable units with which to       
compare all great periods of  time2 the 
oscillations of the isochronous pendulum
 measure its smaller  portions4 ,by     
these invariable standards alone we can 
judge of the slow  changes that other   
elements of the system may have         
undergone in the  lapse of ages4    ,the
 returns of the sun to the same         
meridian1 and to the same equinox or    
solstice1 have been universally adopted 
as the measure of our civil days  and   
years4 ,the solar or astronomical day is
 the time that elapses  between two     
consecutive noons or midnights2 it is   
consequently longer  than the sidereal  
day1 on account of the proper motion of 
the sun during  a revolution of the     
celestial sphere2 but as the sun moves  
with greater  rapidity at the winter    
than at the summer solstice1 the        

astronomical day  is more nearly equal  
to the sidereal day in summer than in   
winter4 ,the  obliquity of the ecliptic 
also affects its duration1 for in the   
equinoxes the arc of the equator is less
 than the corresponding arc of  the     
ecliptic1 and in the solstices it is    
greater4 ,the astronomical day  is      
therefore diminished in the first case1 
and increased in the second4  ,if the   
sun moved uniformly in the equator at   
the rate of #ei' #hc  every day1 the    
solar days would be all equal2 the time 
therefore1 which  is reckoned by the    
arrival of an imaginary sun at the      
meridian1 or of  one which is supposed  
to move in the equator1 is denominated  
mean solar  time1 such as is given by   
clocks and watches in common life3 when 
it is  reckoned by the arrival of the   
real sun at the meridian1 it is apparent
  time1 such as is given by dials4 ,the 
difference between the time shown  by a 
clock and a dial is the equation of time
 given in the ,nautical  ,almanac1 and  

sometimes amounts to as much as sixteen 
minutes4 ,the  apparent and mean time   
coincide four times in the year4        
,astronomers begin the day at noon1 but 
in common reckoning the day  begins at  
midnight4 ,in ,england it is divided    
into twenty-four hours1  which are      
counted by twelve and twelve2 but in    
,france1 astronomers  adopting decimal  
division1 divide the day into ten hours1
 the hour into  one hundred minutes1 and
 the minute into a hundred seconds1     
because of  the facility in computation1
 and in conformity with their system of 
weights and measures4 ,this subdivision 
is not used in common life1 nor  has it 
been adopted in any other country1      
though their scientific  writers still  
employ that division of time4 ,the mean 
length of the day1  though accurately   
determined1 is not sufficient for the   
purposes either  of astronomy or civil  
life4 ,the length of the year is pointed
 out by  nature as a measure of long    
periods2 but the incommensurability that

  exists between the lengths of the day1
 and the revolutions of the sun1        
renders it difficult to adjust the      
estimation of both in whole numbers4    
,if the revolution of the sun were      
accomplished in #cfe days1 all the      
years would be of precisely the same    
number of days1 and would begin and  end
 with the sun at the same point of the  
ecliptic2 but as the sun's  revolution  
includes the fraction of a day1 a civil 
year and a revolution  of the sun have  
not the same duration4 ,since the       
fraction is nearly the  fourth of a day1
 four years are nearly equal to four    
revolutions of the  sun1 so that the    
addition of a supernumerary day every   
fourth year  nearly compensates the     
difference2 but in process of time      
further  correction will be necessary1  
because the fraction is less than the   
fourth of a day4 ,the period of seven   
days1 by far the most permanent         
division of time1 and the most ancient  
monument of astronomical  knowledge1 was

 used by the ,brahmins in ,india with   
the same denominations  employed by us1 
and was alike found in the ,calendars of
 the ,jews1  ,egyptians1 ,arabs1 and    
,assyrians2 it has survived the fall of 
empires1  and has existed among all     
successive generations1 a proof of their
  common origin4    ,the new moon       
immediately following the winter        
solstice in the #gjgth year  of ,rome   
was made the #ast of ,january of the    
first year of ,csar2 the  #beth of      
,december in his #deth year1 is         
considered as the date of ,christ's     
nativity2 and ,csar's #dfth year is     
assumed to be the first of our era4     
,the preceding year is called the first 
year before ,christ by  chronologists1  
but by astronomers it is called the year
 #j4 ,the  astronomical year begins on  
the #cast of ,december at noon2 and the 
date  of an observation expresses the   
days and hours which actually elapsed   
since that time4    ,some remarkable    
astronomical eras are determined by the 

position of the  major axis of the solar
 ellipse4 ,moving at the rate of #faijf 
annually1 it accomplishes a tropical    
revolution in #bjice years4 ,it         
coincided with the line of the equinoxes
 #djjj or #djhi years before the        
,christian era1 much about the time     
chronologists assign for the creation   
of man4 ,in #fdhe the major axis will   
again coincide with the line of the     
equinoxes1 but then the solar perigee   
will coincide with the equinox of       
spring2 whereas at the creation of man  
it coincided with the autumnal  equinox4
 ,in the year #abej the major axis was  
perpendicular to the line  of the       
equinoxes1 and then the solar perigee   
coincided with the solstice  of winter1 
and the apogee with the solstice of     
summer4 ,on that account  ,la ,place    
proposed the year #abej as a universal  
epoch1 and that the  vernal equinox of  
that year should be the first day of the
 first year4    ,the variations in the  
positions of the solar ellipse occasion 

corresponding changes in the length of  
the seasons4 ,in its present  position  
spring is shorter than summer1 and      
autumn longer than winter2  and while   
the solar perigee continues as it now   
is1 between the solstice  of winter and 
the equinox of spring1 the period       
including spring and  summer will be    
longer than that including autumn and   
winter3 in this  century the difference 
is about seven days4 ,these intervals   
will be  equal towards the year #fdhe1  
when the perigee comes to the equinox of
  spring4 ,were the earth's orbit       
circular1 the seasons would be equal2   
their differences arise from the        
eccentricity of the earth's orbit1      
small as it is2 but the changes are so  
gradual as to be imperceptible in  the  
short space of human life4    ,no       
circumstance in the whole science of    
astronomy excites a deeper  interest    
than its application to chronology4     
',whole nations1' says ,la  ,place1     
'have been swept from the earth1 with   

their language1 arts and  sciences1     
leaving but confused masses of ruin to  
mark the place where  mighty cities     
stood2 their history1 with the exception
 of a few doubtful  traditions1 has     
perished2 but the perfection of their   
astronomical  observations marks their  
high antiquity1 fixes the periods of    
their  existence1 and proves that even  
at that early period they must have made
  considerable progress in science4'    
,the ancient state of the heavens may   
now be computed with great  accuracy2   
and by comparing the results of         
computation with ancient  observations1 
the exact period at which they were made
 may be verified  if true1 or if false1 
their error may be detected4 ,if the    
date be  accurate1 and the observation  
good1 it will verify the accuracy of    
modern tables1 and show to how many     
centuries they may be extended1  without
 the fear of error4 ,a few examples will
 show the importance of  this subject4  
,at the solstices the sun is at his     

greatest distance from the equator1     
consequently his declination at these   
times is equal to the obliquity of  the 
ecliptic1 which in former times was     
determined from the meridian  length of 
the shadow of the style of a dial on the
 day of the solstice4  ,the lengths of  
the meridian shadow at the summer and   
winter solstice are  recorded to have   
been observed at the city of ,layang1 in
 ,china1 #aajj  years before the        
,christian era4 ,from these1 the        
distances of the sun  from the zenith of
 the city of ,layang are known4 ,half   
the sum of these  zenith distances      
determines the latitude1 and half their 
difference  gives the obliquity of the  
ecliptic at the period of the           
observation2  and as the law of the     
variation in the obliquity is known1    
both the time  and place of the         
observations have been verified by      
computation from  modern tables4 ,thus  
the ,chinese had made some advances in  
the science of  astronomy at that early 

period2 the whole chronology of the     
,chinese is  founded on the observations
 of eclipses1 which prove the existence 
of  that empire for more than #dgjj     
years4 ,the epoch of the lunar tables of
  the ,indians1 supposed by ,bailly to  
be #cjjj before the ,christian era1 was 
proved by ,la ,place from the           
acceleration of the moon1 not to be more
  ancient than the time of ,ptolemy4    
,the great inequality of ,jupiter and   
,saturn whose cycle embraces #ibi years1
 is peculiarly fitted for marking  the  
civilization of a people4 ,the ,indians 
had determined the mean  motions of     
these two planets in that part of their 
periods when the  apparent menu motion  
of ,saturn was at the slowest1 and that 
of ,jupiter  the most rapid4 ,the       
periods in which that happened were     
#cajb years  before the ,christian era1 
and the year #adia after it4    ,the    
returns of comets to their perihelia may
 possibly mark the present  state of    
astronomy to future ages4    ,the places

 of the fixed stars are affected by the 
precession of the  equinoxes2 and as the
 law of that variation is known1 their  
positions at  any time may be computed4 
,now ,eudoxus1 a contemporary of ,plato1
 mentions  a star situate in the pole of
 the equator1 and from computation it   
appears that   ,draconis was not very   
far from that place about #cjjj  years  
ago2 but as ,eudoxus lived only about   
#baej years ago1 he must have  described
 an anterior state of the heavens1      
supposed to be the same that  was       
determined by ,chiron1 about the time of
 the siege of ,troy4 ,every             
circumstance concurs in showing that    
astronomy was cultivated in the  highest
 ages of antiquity4    ,a knowledge of  
astronomy leads to the interpretation of
 hieroglyphical  characters1 since      
astronomical signs are often found on   
the ancient  ,egyptian monuments1 which 
were probably employed by the priests to
  record dates4 ,on the ceiling of the  
portico of a temple among the ruins  of 

,tentyris1 there is a long row of       
figures of men and animals1  following  
each other in the some direction among  
these are the twelve  signs of the      
zodiac1 placed according to the motion  
of the sun3 it is  probable that the    
first figure in the procession          
represents the  beginning of the year4  
,now the first is the ,lion as if coming
 out of the  temple2 and as it is well  
known that the agricultural year of the 
,egyptians commenced at the solstice of 
summer1 the epoch of the  inundations of
 the ,nile1 if the preceding hypothesis 
be true1 the  solstice at the time the  
temple was built must have happened in  
the  constellation of the lion2 but as  
the solstice now happens #ba #f' north  
of the constellation of the ,twins1 it  
is easy to compute that the zodiac  of  
,tentyris must have been made #djjj     
years ago4    ,the author had occasion  
to witness an instance of this most     
interesting  application of astronomy1  
in ascertaining the dale of a papyrus   

sent  from ,egypt by ,mr4 ,salt1 in the 
hieroglyphical researches of the late   
,dr4  ,thomas ,young1 whose profound and
 varied acquirements do honour not only 
to his country1 but to the age in which 
he lived4 ,the manuscript was  found in 
a mummy case2 it proved to be a         
horoscope of the age of  ,ptolemy1 and  
its antiquity was determined from the   
configuration of the  heavens at the    
time of its construction4    ,the form  
of the earth furnishes a standard of    
weights and measures for  the ordinary  
purposes of life1 as well as for the    
determination of the  masses and        
distances of the heavenly bodies4 ,the  
length of the pendulum  vibrating       
seconds in the latitude of ,london forms
 the standard of the  ,british measure  
of extension4 ,its length oscillating in
 vacuo at the  temperature of #fb of    
,fahrenheit1 and reduced to the level of
 the sea1  was determined by ,captain   
,kater1 in parts of the imperial        
standard yard1  to be #ci4achg inches4  

,the weight of a cubic inch of water at 
the  temperature of #fb ,fahrenheit1    
barometer #cj1 was also determined in   
parts of the imperial troy pound1 whence
 a standard both of weight and  capacity
 is deduced4 ,the ,french have adopted  
the metre for their unit of  linear     
measure1 which is the ten millionth part
 of that quadrant of the  meridian      
passing through ,formentera and         
,greenwich1 the middle of which  is     
nearly in the forty-fifth degree of     
latitude4 ,should the national          
standards of the two countries be lost  
in the vicissitudes of human  affairs1  
both may be recovered1 since they are   
derived from natural  standards presumed
 to be invariable4 ,the length of the   
pendulum would be  found again with more
 facility than the metre2 but as no     
measure is  mathematically exact1 an    
error in the original standard may at   
length  become sensible in measuring a  
great extent1 whereas the error that    
must  necessarily arise in measuring the

 quadrant of the meridian is rendered   
totally insensible by subdivision in    
taking its ten millionth part4 ,the     
,french have adopted the decimal        
division not only in time1 but in their 
degrees1 weights1 and measures1 which   
affords very great facility in          
computation4 ,it has not been adopted by
 any other people2 though nothing  is   
more desirable than that all nations    
should concur in using the same         
division and standards1 not only on     
account of the convenience1 but as      
affording a more definite idea of       
quantity4 ,it is singular that the      
decimal division of the day1 of degrees1
 weights and measures1 was  employed in 
,china #djjj years ago2 and that1 at the
 time ,ibn ,yunus made  his observations
 at ,cairo1 about the year #ajjj1 the   
,arabians were in the  habit of         
employing the vibrations of the pendulum
 in their astronomical  observations4   
,one of the most immediate and striking 
effects of a gravitating force  external

 to the earth is the alternate rise and 
fall of the surface of  the sea twice in
 the course of a lunar day1 or #bd;h    
#ejm #dhs of mean solar  time4 ,as it   
depends on the action of the sun and    
moon1 it is classed  among astronomical 
problems1 of which it is by far the most
 difficult  and the least satisfactory4 
,the form of the surface of the ocean in
  equilibrio1 when revolving with the   
earth round its axis1 is an  ellipsoid  
flattened at the poles2 but the action  
of the sun and moon1  especially of the 
moon1 disturbs the equilibrium of the   
ocean4    ,if the moon attracted the    
centre of gravity of the earth and all  
its  particles with equal and parallel  
forces1 the whole system of the earth   
and the waters that cover it1 would     
yield to these forces with a common     
motion1 and the equilibrium of the seas 
would remain undisturbed4 ,the          
difference of the forces1 and the       
inequality of their directions1 alone   
trouble the equilibrium4    ,it is      

proved by daily experience1 as well as  
by strict mechanical  reasoning1 that if
 a number of waves or oscillations be   
excited in a  fluid by different forces1
 each pursues its course1 and has its   
effect  independently of the rest4 ,now 
in the tides there are three distinct   
kinds of oscillations1 depending on     
different causes1 producing their       
effects independently of each other1    
which may therefore be estimated        
separately4    ,the oscillations of the 
first kind which are very small1 are    
independent  of the rotation of the     
earth2 and as they depend on the motion 
of the  disturbing body in its orbit1   
they are of long periods4 ,the second   
kind  of oscillations depends on the    
rotation of the earth1 therefore their  
period is nearly a day3 and the         
oscillations of the third kind depend on
  an angle equal to twice the angular   
rotation of the earth2 and  consequently
 happen twice in twenty-four hours4 ,the
 first afford no  particular interest1  

and are extremely small2 but the        
difference of two  consecutive tides    
depends on the second4 ,at the time of  
the solstices1  this difference which1  
according to ,newton's theory1 ought to 
be very  great1 is hardly sensible on   
our shores4 ,la ,place has shown that   
this  discrepancy arises from the depth 
of the sea1 and that if the depth were  
uniform1 there would be no difference in
 the consecutive tides1 were it  not for
 local circumstances3 it follows        
therefore1 that as this  difference is  
extremely small1 the sea1 considered in 
a large extent1  must be nearly of      
uniform depth1 that is to say1 there is 
a certain mean  depth from which the    
deviation is not great4 ,the mean depth 
of the  ,pacific ,ocean is supposed to  
be about four miles1 that of the        
,atlantic  only three4 ,from the formul 
which determine the difference of the   
consecutive tides it is also proved that
 the precession of the  equinoxes1 and  
the nutation in the earth's axis1 are   

the same as if the  sea formed one solid
 mass with the earth4    ,the third kind
 of oscillations are the semidiurnal    
tides1 so remarkable  on our coasts2    
they are occasioned by the combined     
action of the sun and  moon1 but as the 
effect of each is independent of the    
other1 they may be  considered          
separately4    ,the particles of water  
under the moon are more attracted than  
the centre  of gravity of the earth1 in 
the inverse ratio of the square of the  
distances2 hence they have a tendency to
 leave the earth1 but are  retained by  
their gravitation1 which this tendency  
diminishes4 ,on the  contrary1 the moon 
attracts the centre of the earth more   
powerfully than  she attracts the       
particles of water in the hemisphere    
opposite to her2  so that the earth has 
a tendency to leave the waters but is   
retained by  gravitation1 which this    
tendency again diminishes4 ,thus the    
waters  immediately under the moon are  
drawn from the earth at the same time   

that the earth is drawn from those which
 are diametrically opposite to  her2 in 
both instances producing an elevation of
 the ocean above the  surface of        
equilibrium of nearly the same height2  
for the diminution of  the gravitation  
of the particles in each position is    
almost the same1 on  account of the     
distance of the moon being great in     
comparison of the  radius of the earth4 
,were the earth entirely covered by the 
sea1 the  water thus attracted by the   
moon would assume the form of an oblong 
spheroid1 whose greater axis would point
 towards the moon1 since the  columns of
 water under the moon and in the        
direction diametrically  opposite to her
 are rendered lighter1 in consequence of
 the diminution  of their gravitation in
 order to preserve the equilibrium1 the 
axes #ij  distant would be shortened4   
,the elevation1 on account of the       
smaller  space to which it is confined1 
is twice as great as the depression1    
because the contents of the spheroid    

always remain the same4 ,the effects  of
 the sun's attraction are in all        
respects similar to those of the        
moon's1 though really less in degree1 on
 account of his distance2 he  therefore 
only modifies the form of this spheroid 
a little4 ,if the  waters were capable  
of instantly assuming the form of       
equilibrium1 that  is1 the form of the  
spheroid1 its summit would always point 
to the moon1  notwithstanding the       
earth's rotation2 but on account of     
their  resistance1 the rapid motion     
produced in them by rotation prevents   
them  from assuming at every instant the
 form which the equilibrium of the      
forces acting on them requires4 ,hence1 
on account of the inertia of the        
waters1 if the tides be considered      
relatively to the whole earth and  open 
sea1 there is a meridian about #cj      
eastward of the moon1 where it  is      
always high water both in the hemisphere
 where the moon is1 and in  that which  
is opposite4 ,on the west side of this  

circle the tide is  flowing1 on the east
 it is ebbing1 and on the meridian at   
#ij distant1  it is everywhere low      
water4 ,it is evident that these tides  
must happen  twice in a day1 since in   
that time the rotation of the earth     
brings the  same point twice under the  
meridian of the moon1 once under the    
superior  and once under the inferior   
meridian4    ,in the semidiurnal tides  
there are two phenomena particularly to 
be  distinguished1 one that happens     
twice in a month1 and the other twice in
  a year4    ,the first phenomenon is1  
that the tides are much increased in the
  syzigies1 or at the time of new and   
full moon4 ,in both cases the sun and   
moon are in the same meridian1 for when 
the moon is new they are in             
conjunction1 and when she is full they  
are in opposition4 ,in each of  these   
positions their action is combined to   
produce the highest or  spring tides    
under that meridian1 and the lowest in  
those points that  are #ij distant4 ,it 

is observed that the higher the sea     
rises in the  full tide1 the lower it is
 in the ebb4 ,the neap tides lake place 
when  the moon is in quadrature1 they   
neither rise so high nor sink so low as 
the spring tides4 ,the spring tides are 
much increased when the moon is  in     
perigee4 ,it is evident that the spring 
tides must happen twice a  month1 since 
in that time the moon is once new and   
once full4    ,the second phenomenon in 
the tides is the augmentation which     
occurs at  the time of the equinoxes    
when the sun's declination is zero1     
which  happens twice every year4 ,the   
greatest tides take place when a new or 
full moon happens1 near the equinoxes   
while the moon is in perigee4 ,the      
inclination of the moon's orbit on the  
ecliptic is #e #i'2 hence in  the       
equinoxes the action of the moon would  
be increased if her node were  to       
coincide with her perigee4 ,the         
equinoctial gales often raise these     
tides to a great height4 ,beside these  

remarkable variations1 there are  others
 arising from the declination of the    
moon1 which has a great  influence on   
the ebb and flow of the waters4    ,both
 the height and time of high water are  
thus perpetually changing2  therefore1  
in solving the problem1 it is required  
to determine the  heights to which they 
rise1 the times at which they happen1   
and the  daily variations4    ,the      
periodic motions of the waters of the   
ocean on the hypothesis of an  ellipsoid
 of revolution entirely covered by the  
sea1 are very far from  according with  
observation2 this arises from the very  
great  irregularities in the surface of 
the earth1 which is but partially       
covered by the sea1 the variety in the  
depths of the ocean1 the manner  in     
which it is spread out on the earth1 the
 position and inclination of  the       
shores1 the currents1 the resistance the
 waters meet with1 all of  them causes  
which it is impossible to estimate1 but 
which modify the  oscillations of the   

great mass of the ocean4 ,however1      
amidst all these  irregularities1 the   
ebb and flow of the sea maintain a ratio
 to the  forces producing them          
sufficient to indicate their nature1 and
 to verify  the law of the attraction of
 the sun and moon on the sea4 ,la ,place
  observes1 that the investigation of   
such relations between cause and  effect
 is no less useful in natural philosophy
 than the direct solution  of problems1 
either to prove the existence of the    
causes1 or trace the  laws of their     
effects4 ,like the theory of            
probabilities1 it is a happy  supplement
 to the ignorance and weakness of the   
human mind4 ,thus the  problem of the   
tides does not admit of a general       
solution2 it is  certainly necessary to 
analyse the funeral phenomena which     
ought to  result from the attraction of 
the sun and moon1 but these must be     
corrected in each particular case by    
those local observations which are      
modified by the extent and depth of the 

sea1 and the peculiar  circumstances of 
the port4    ,since the disturbing      
action of the sun and moon can only     
become sensible  in a very great extent 
of water1 it is evident that the        
,pacific ocean is  one of the principal 
sources of our tides2 but in consequence
 of the  rotation of the earth1 and the 
inertia of the ocean1 high water does   
not  happen till some time after the    
moon's southing4 ,the tide raised in    
that  world of waters is transmitted to 
the ,atlantic1 and from that sea it     
moves in a northerly direction along the
 coasts of ,africa and ,europe1         
arriving later and later at each place4 
,this great wave however is  modified by
 the tide raised in the ,atlantic1 which
 sometimes combines  with that from the 
,pacific in raising the sea1 and        
sometimes is in  opposition to it1 so   
that the tides only rise in proportion  
to their  difference4 ,this great       
combined wave1 reflected by the shores  
of the  ,atlantic1 extending nearly from

 pole to pole1 still coming northward1  
occurs through the ,irish and ,british  
channels into the ,north sea1 so  that  
the tides in our ports are modified by  
those of another hemisphere4  ,thus the 
theory of the tides in each port1 both  
as to their height and  the times at    
which they take place1 is really a      
matter of experiment1  and can only be  
perfectly determined by the mean of a   
very great number  of observations      
including several revolutions of the    
moon's nodes4    ,the height to which   
the tides rise is much greater in narrow
 channels  than in the open sea1 on     
account of the obstructions they meet   
with4 ,in  high latitudes where the     
ocean is less directly under the        
influence of  the luminaries1 the rise  
and fall of the sea is inconsiderable1  
so that1  in all probability1 there is  
no tide at the poles1 or only a small   
annual and monthly one4 ,the ebb and    
flow of the sea are perceptible in      
rivers to a very great distance from    

their estuaries4 ,in the straits of     
,pauxis1 in the river of the ,amazons1  
more than five hundred miles from  the  
sea1 the tides are evident4 ,it requires
 so many days for the tide to  ascend   
this mighty stream1 that the returning  
tides meet a succession of  those which 
are coming up2 so that every possible   
variety occurs in some  part or other of
 its shores1 both as to magnitude and   
time4 ,it requires  a very wide expanse 
of water to accumulate the impulse of   
the sun and  moon1 so as to render their
 influence sensible2 on that account the
  tides in the ,mediterranean and ,black
 ,sea are scarcely perceptible4         
,these perpetual commotions in the      
waters of the ocean are occasioned by   
forces that bear a very small proportion
 to terrestrial gravitation3 the  sun's 
action in raising the ocean is only the 
#a_/chddhjjj of gravitation  at the     
earth's surface1 and the action of the  
moon is little more than  twice as much 
these forces being in the ratio of #a to

 #b4ceccc4 ,from this  ratio the mass of
 the moon is found to be only #a_/ae    
part of that of the  earth4 ,the initial
 state of the ocean has no influence on 
the tides2  for whatever its primitive  
conditions may have been1 they must soon
 have  vanished by the friction and     
mobility of the fluid4 ,one of the most 
remarkable circumstances in the theory  
of the tides is the assurance  that in  
consequence of the density of the sea   
being only one-fifth of  the mean       
density of the earth1 the stability of  
the equilibrium of the  ocean never can 
be subverted by any physical cause      
whatever4 ,a general  inundation arising
 from the mere instability of the ocean 
is therefore  impossible4    ,the       
atmosphere when in equilibrio is an     
ellipsoid flattened at the poles  from  
its rotation with the earth3 in that    
state its strata are of  uniform density
 at equal heights above the level of the
 sea1 and it is  sensibly of finite     
extent1 whether it consists of particles

 infinitely  divisible or not4 ,on the  
latter hypothesis it must really be     
finite2 and  even if the particles of   
matter be infinitely divisible1 it is   
known by  experience to be of extreme   
tenuity at very small heights4 ,the     
barometer  rises in proportion to the   
superincumbent pressure4 ,now at the    
temperature of melting ice1 the density 
of mercury is to that of air as  #ajcbj 
to #a2 and as the mean height of the    
barometer is #bi4ebh inches1  the height
 of the atmosphere by simple proportion 
is #cjdjg feet1 at the  mean temperature
 of #fb1 or #cdaec feet1 which is       
extremely small1 when  compared with the
 radius of the earth4 ,the action of the
 sun and moon  disturbs the equilibrium 
of the atmosphere1 producing            
oscillations  similar to those in the   
ocean1 which occasion periodic          
variations in the  heights of the       
barometer4 ,these1 however1 are so      
extremely small1 that  their existence  
in latitudes so far removed from the    

equator is  doubtful2 a series of       
observations within the tropics can     
alone decide  this delicate point4 ,la  
,place seems to think that the flux and 
reflux  distinguishable at ,paris may be
 occasioned by the rise and fall of the 
ocean1 which forms a variable base to so
 great a portion of the  atmosphere4    
,the attraction of the sun and moon has 
no sensible effect on the trade  winds2 
the heat of the sun occasions these     
aerial currents1 by rarefying  the air  
at the equator1 which causes the cooler 
and more dense part of  the atmosphere  
to rush along the surface of the earth  
to the equator1  while that which is    
heated is carried along the higher      
strata to the  poles1 forming two       
currents in the direction of the        
meridian4 ,but the  rotatory velocity of
 the air corresponding to its           
geographical situation  decreases       
towards the poles2 in approaching the   
equator it must  therefore revolve more 
slowly than the corresponding parts of  

the earth1  and the bodies on the       
surface of the earth must strike against
 it with  the excess of their velocity1 
and by its reaction they will meet with 
a  resistance contrary to their motion  
of rotation2 so that the wind will      
appear1 to a person supposing himself to
 be at rest1 to blow in a  contrary     
direction to the earth's rotation1 or   
from east to west1 which  is the        
direction of the trade winds4 ,the      
atmosphere scatters the sun's  rays1 and
 gives all the beautiful tints and      
cheerfulness of day4 ,it  transmits the 
blue light in greatest abundance2 the   
higher we ascend1  the sky assumes a    
deeper hue1 but in the expanse of space 
the sun and  stars must appear like     
brilliant specks in profound blackness4 
,the sun and most of the planets appear 
to be surrounded with atmospheres  of   
considerable density4 ,the attraction of
 the earth has probably  deprived the   
moon of hers1 for the refraction of the 
air at the surface  of the earth is at  

least a thousand times as great as at   
the moon4 ,the  lunar atmosphere1       
therefore1 must be of a greater degree  
of rarity than  can be produced by our  
best air-pumps2 consequently no         
terrestrial  animal could exist in it4  
,many philosophers of the highest       
authority concur in the belief that     
light consists in the undulations of a  
highly elastic ethereal medium          
pervading space1 which1 communicated to 
the optic nerves produce the  phenomena 
of vision4 ,the experiments of our      
illustrious countryman1 ,dr4  ,thomas   
,young1 and those of the celebrated     
,fresnel1 show that this theory  accords
 better with all the observed phenomena 
than that of the emission  of particles 
from the luminous body4 ,as sound is    
propagated by the  undulations of the   
air1 its theory is in a great many      
respects similar  to that of light4 ,the
 grave or low tones are produced by very
 slow  vibrations1 which increase in    
frequency progressively as the note     

becomes more acute4 ,when the vibrations
 of a musical chord1 for example1  are  
less than sixteen in a second1 it will  
not communicate a continued  sound to   
the ear2 the vibrations or pulses       
increase in number with the  acuteness  
of the note1 till at last all sense of  
pitch is lost4 ,the  whole extent of    
human hearing1 from the lowest notes of 
the organ to the  highest known cry of  
insects1 as of the cricket1 includes    
about nine  octaves4    ,the undulations
 of light are much more rapid than those
 of sound1 but  they are analogous in   
this respect1 that as the frequency of  
the  pulsations in sound increases from 
the low tones to the higher1 so those   
of light augment in frequency1 from the 
red rays of the solar spectrum  to the  
extreme violet4 ,by the experiments of  
,sir ,william ,herschel1 it  appears    
that the heat communicated by the       
spectrum increases from the  violet to  
the red rays2 but that the maximum of   
the hot invisible rays  is beyond the   

extreme red4 ,heat in all probability   
consists1 like light  and sound1 in the 
undulations of an elastic medium4 ,all  
the principal  phenomena of heat may    
actually be illustrated by a comparison 
with those  of sound4 ,the excitation of
 heat and sound are not only similar1   
but  often identical1 as in friction and
 percussion2 they are both  communicated
 by contact and by radiation2 and ,dr4  
,young observes1 that  the effect of    
radiant heat in raising the temperature 
of a body upon  which it falls1         
resembles the sympathetic agitation of a
 string1 when  the sound of another     
string1 which is in unison with it1 is  
transmitted  to it through the air4     
,light1 heat1 sound1 and the waves of   
fluids are  all subject to the same laws
 of reflection1 and1 indeed1 their      
undulating theories are perfectly       
similar4 ,if1 therefore1 we may judge   
from analogy1 the undulations of the    
heat producing rays must be less        
frequent than those of the extreme red  

of the solar spectrum2 but if the       
analogy were perfect1 the interference  
of two hot rays ought to produce  cold1 
since darkness results from the         
interference of two undulations of      
light1 silence ensues from the          
interference of two undulations of      
sound2  and still water1 or no tide1 is 
the consequence of the interference of  
two tides4    ,the propagation of sound 
requires a much denser medium than that 
of  either light or heat2 its intensity 
diminishes as the rarity of the air     
increases2 so that1 at a very small     
height above the surface of the  earth1 
the noise of the tempest ceases1 and the
 thunder is heard no more  in those     
boundless regions where the heavenly    
bodies accomplish their  periods in     
eternal and sublime silence4    ,what   
the body of the sun may be1 it is       
impossible to conjecture2 but he  seems 
to be surrounded by an ocean of flame   
through which his dark  nucleus appears 
like black spots1 often of enormous     

size4 ,the solar  rays1 which probably  
arise from the chemical processes that  
continually  take place at his surface1 
are transmitted through space in all    
directions2 but1 notwithstanding the    
sun's magnitude1 and the  inconceivable 
heat that must exist where such         
combustion is going on1 as  the         
intensity both of his light and heat    
diminishes with the square of  the      
distance1 his kindly influence can      
hardly be felt at the boundaries  of our
 system4 ,much depends on the manner in 
which the rays fall1 as we  readily     
perceive from the different climates on 
our globe4 ,in winter the  earth is     
nearer the sun by #a_/cjth than in      
summer1 but the rays strike  the        
northern hemisphere more obliquely in   
winter than in the other half  of the   
year4 ,in ,uranus the sun must be seen  
like a small but brilliant  star1 not   
above the hundred and fiftieth part so  
bright as he appears  to us2 that is    
however #bjjj times brighter than our   

moon to us1 so  that he really is a sun 
to ,uranus1 and probably imparts some   
degree  of warmth4 ,but if we consider  
that water would not remain fluid in any
  part of ,mars1 even at his equator1   
and that in the temperate zones of  the 
same planet even alcohol and quicksilver
 would freeze1 we may form  some idea of
 the cold that must reign in ,uranus1   
unless indeed the  ether has a          
temperature4 ,the climate of ,venus more
 nearly resembles  that of the earth1   
though1 excepting perhaps at her poles1 
much too  hot for animal and vegetable  
life as they exist here2 but in ,mercury
  the mean heat1 arising only from the  
intensity of the sun's rays1  must be   
above that of boiling quick-silver1 and 
water would boil even  at his poles4    
,thus the planets1 though kindred with  
the earth in  motion and structure1 are 
totally unfit for the habitation of such
  a being as man4    ,the direct light  
of the sun has been estimated to be     
equal to that of  #eefc wax candles of a

 moderate size1 supposed to be placed at
 the  distance of one foot from the     
object3 that of the moon is probably    
only  equal to the light of one candle  
at the distance of twelve feet2         
consequently the light of the sun is    
more than three hundred thousand  times 
greater than that of the moon2 for which
 reason the light of the  moon imparts  
no heat1 even when brought to a focus by
 a mirror4    ,in adverting to the      
peculiarities in the form and nature of 
the earth  and planets1 it is impossible
 to pass in silence the magnetism of the
  earth1 the director of the mariner's  
compass1 and his guide through the      
ocean4 ,this property probably arises   
from metallic iron in the interior  of  
the earth1 or from the circulation of   
currents of electricity round  it3 its  
influence extends over every part of its
 surface1 but its  accumulation and     
deficiency determine the two poles of   
this great  magnet1 which are by no     
means the same as the poles of the      

earth's  rotation4 ,in consequence of   
their attraction and repulsion1 a needle
  freely suspended1 whether it be       
magnetic or not1 only remains in        
equilibrio when in the magnetic         
meridian1 that is1 in the plane which   
passes through the north and south      
magnetic poles4 ,there are places  where
 the magnetic meridian coincides with   
the terrestrial meridian2 in  these a   
magnetic needle freely suspended1 points
 to the true north1 but  if it be       
carried successively to different places
 on the earth's  surface1 its direction 
will deviate sometimes to the east and  
sometimes  to the west of north4 ,lines 
drawn on the globe through all the      
places  where the needle points due     
north and south1 are called lines of no 
variation1 and are extremely            
complicated4 ,the direction of the      
needle is  not even constant in the same
 place1 but changes in a few years1     
according to a law not yet determined4  
,in #afeg1 the line of no variation     

passed through ,london4 ,in the year    
#ahai1 ,captain ,parry1 in his voyage to
  discover the north-west passage round 
,america1 sailed directly over the      
magnetic pole2 and in #ahbd1 ,captain   
,lyon1 when on en expedition for the    
same purpose1 found that the variation  
of the compass was #cg #cj'  west1 and  
that the magnetic pole was then situate 
in #fc #bf' #ea  north latitude1 and in 
#hj #ea' #be west longitude4 ,it appears
  however from later researches that the
 law of terrestrial magnetism is  of    
considerable complication1 and the      
existence of more than one  magnetic    
pole in either hemisphere has been      
rendered highly probable4  ,the needle  
is also subject to diurnal variations2  
in our latitudes it  moves slowly       
westward from about three in the morning
 till two1 and  returns to its former   
position in the evening4    ,a needle   
suspended so as only to be moveable in  
the vertical plane1 dips  or become more
 and more inclined to the horizon the   

nearer it is brought  to the magnetic   
pole4 ,captain ,lyon found that the dip 
in the latitude  and longitude mentioned
 was #hf #cb'4 ,what properties the     
planets may  have in this respect1 it is
 impossible to know1 but it is probable 
that  the moon has become highly        
magnetic1 in consequence of her         
proximity to  the earth1 and because her
 greatest diameter always points towards
 it4    ,the passage of comets has never
 sensibly disturbed the stability of the
  solar system2 their nucleus is rare1  
and their transit so rapid1 that  the   
time has not been long enough to admit  
of a sufficient accumulation  of impetus
 to produce a perceptible effect4 ,the  
comet of #aggj passed  within #hjjjj    
miles of the earth without even         
affecting our tides1 and  swept through 
the midst of ,jupiter's satellites      
without deranging the  motions of those 
little moons4 ,had the mass of that     
comet been equal to  the mass of the    
earth1 its disturbing action would have 

shortened the  year by the ninth of a   
day2 but1 as ,delambre's computations   
from the  ,greenwich observations of the
 sun1 show that the length of the year  
has  not been sensibly affected by the  
approach of the comet4 ,la ,place proved
  that its mass could not be so much as 
the #ejjjth part of that of the  earth4 
,the paths of comets have every possible
 inclination to the plane  of the       
ecliptic1 and unlike the planets1 their 
motion is frequently  retrograde4       
,comets are only visible when near their
 perihelia4 ,then  their velocity is    
such that its square is twice as great  
as that of a  body moving in a circle at
 the same distance2 they consequently   
remain a  very short time within the    
planetary orbits2 and as all the conic  
sections of the same focal distance     
sensibly coincide through a small  arc  
on each side of the extremity of their  
axis1 it is difficult to  ascertain in  
which of these curves the comets move1  
from observations  made1 as they        

necessarily must be1 at their perihelia3
 but probably they  all move in         
extremely eccentric ellipses1 although1 
in most cases1 the  parabolic curve     
coincides most nearly with their        
observed motions4 ,even  if the orbit be
 determined with all the accuracy that  
the case admits  of1 it may be          
difficult1 or even impossible1 to       
recognise a comet on its  return1       
because its orbit would be very much    
changed if it passed near  any of the   
large planets of this or of any other   
system1 in consequence  of their        
disturbing energy1 which would be very  
great on bodies of so  rare a nature4   
,halley and ,clairaut predicted that1 in
 consequence of the  attraction of      
,jupiter and ,saturn1 the return of the 
comet of #agei would  be retarded #fah  
days1 which was verified by the event as
 nearly as could  be expected4    ,the  
nebulous appearance of comets is perhaps
 occasioned by the vapours  which the   
solar heat raises at their surfaces in  

their passage at the  perihelia1 and    
which are again condensed as they recede
 from the sun4  ,the comet of #afhj when
 in its perihelion was only at the      
distance of  one-sixth of the sun's     
diameter1 or about #adhjjj miles from   
its surface2  it consequently would be  
exposed to a heat #bgejj times greater  
than that  received by the earth4 ,as   
the sun's heat is supposed to be in     
proportion  to the intensity of his     
height1 it is probable that a degree of 
heat so  very intense would be          
sufficient to convert into vapour every 
terrestrial substance with which we are 
acquainted4    ,in those positions of   
comets where only half of their         
enlightened  hemisphere ought to be     
seen1 they exhibit no phases even when  
viewed  with high magnifying powers4    
,some slight indications however were   
once  observed by ,hevelius and ,la     
,hire in #afhb2 and in #ahaa ,sir       
,william  ,herschel discovered a small  
luminous point1 which he concluded to be

 the  disc of the comet4 ,in general    
their masses are so minute1 that they   
have  no sensible diameters1 the nucleus
 being principally formed of denser     
strata of the nebulous matter1 but so   
rare that stars have been seen  through 
them4 ,the transit of a comet over the  
sun's disc would afford  the best       
information on this point4 ,it was      
computed that such an event  was to take
 place in the year #afbg2 unfortunately 
the sun was hid by  clouds in this      
country1 but it was observed at ,viviers
 and at ,marseilles  at the time the    
comet must have been on it1 but no spot 
was seen4 ,the  tails are often of very 
great length1 and are generally situate 
in the  planes of their orbits2 they    
follow them in their descent towards the
  sun1 but precede them in their return1
 with a small degree of curvature2  but 
their extent and form must vary in      
appearance1 according to the  position  
of their orbits with regard to the      
ecliptic4 ,the tail of the  comet of    

#afhj appeared1 at ,paris1 to extend    
over sixty-two degrees4 ,the  matter of 
which the tail is composed must be      
extremely buoyant to  precede a body    
moving with such velocity2 indeed the   
rapidity of its  ascent cannot be       
accounted for4 ,the nebulous part of    
comets diminishes  every time they      
return to their perihelia2 after        
frequent returns they  ought to lose it 
altogether1 and present the appearance  
of a fixed  nucleus2 this ought to      
happen sooner in comets of short        
periods4 ,la  ,place supposes that the  
comet of #afhb must be approaching      
rapidly to  that state4 ,should the     
substances be altogether or even to a   
great  degree evaporated1 the comet wilt
 disappear for ever4 ,possibly comets   
may have vanished from our view sooner  
than they otherwise would have  done    
from this cause4 ,of about six hundred  
comets that have been seen at  different
 times1 three are now perfectly         
ascertained to form part of our  system2

 that is to say1 they return to the sun 
at intervals of #gf1 #f #a_/c1  and #c  
#a_/d years nearly4    ,a hundred and   
forty comets have appeared within the   
earth's orbit during  the last century  
that have not again been seen2 if a     
thousand years be  allowed as the       
average period of each1 it may be       
computed by the theory  of              
probabilities1 that the whole number    
that range within the earth's  orbit    
must be #adjj2 but ,uranus being twenty 
times more distant1 there  may be no    
less than #aa1bjj1jjj comets that come  
within the known extent  of our system4 
,in such a multitude of wandering bodies
 it is just  possible that one of them  
may come in collision with the earth2   
but even  if it should1 the mischief    
would be local1 and the equilibrium soon
  restored4 ,it is however more probable
 that the earth would only be  deflected
 a little from its course by the near   
approach of the comet1  without being   
touched4 ,great as the number of comets 

appears to be1 it  is absolutely nothing
 when compared to the number of the     
fixed stars4  ,about two thousand only  
are visible to the naked eye1 but when  
we view  the heavens with a telescope1  
their number seems to be limited only by
  the imperfection of the instrument4   
,in one quarter of an hour ,sir         
,william ,herschel estimated that       
#aafjjj stars passed through the field  
of  his telescope1 which subtended an   
angle of #ae'4 ,this however was  stated
 as a specimen of extraordinary         
crowding2 but at an average the  whole  
expanse of the heavens must exhibit     
about a hundred millions of  fixed stars
 that come within the reach of          
telescopic vision4    ,many of the stars
 have a very small progressive motion1  
especially   ,cassiopeia and #fa ,cygni1
 both small stars2 and1 as the sun is   
decidedly  a star1 it is an additional  
reason for supposing the solar system to
 be  in motion4 ,the distance of the    
fixed stars is too great to admit of    

their exhibiting a sensible disc2 but in
 all probability they are  spherical1   
and must certainly be so1 if gravitation
 pervades all space4  ,with a fine      
telescope they appear like a point of   
light2 their twinkling  arises from     
sudden changes in the refractive power  
of the air1 which  would not be sensible
 if they had discs like the planets4    
,thus we can  learn nothing of the      
relative distances of the stars from us 
and from  one another1 by their apparent
 diameters2 but their annual parallax   
being insensible1 shows that we must be 
one hundred millions of millions  of    
miles from the nearest2 many of them    
however must be vastly more  remote1 for
 of two stars that appear close         
together1 one may be far  beyond the    
other in the depth of space4 ,the light 
of ,sirius1 according  to the           
observations of ,mr4 ,herschel1 is #cbd 
times greater than that of a  star of   
the sixth magnitude2 if we suppose the  
two to be really of the  same size1     

their distances from us must be in the  
ratio of #eg4c to #a1  because light    
diminishes as the square of the distance
 of the luminous  body increases4    ,of
 the absolute magnitude of the stars1   
nothing is known1 only that many  of    
them must be much larger than the sun1  
from the quantity of light  emitted by  
them4 ,dr4 ,wollaston determined the    
approximate ratio that the  light of a  
wax candle bears to that of the sun1    
moon1 and stars1 by  comparing their    
respective images reflected from small  
glass globes  filled1 with mercury1     
whence a comparison was established     
between the  quantities of light emitted
 by the celestial bodies themselves4 ,by
 this  method he found that the light of
 the sun is about twenty millions of    
millions of times greater than that of  
,sirius1 the brightest1 and  supposed to
 be the nearest of the fixed stars4 ,if 
,sirius had a parallax  of half a       
second1 its distance from the earth     
would be #ebedha times the  distance of 

the sun from the earth2 and therefore   
,sirius1 placed where  the sun is1 would
 appear to us to be #c4g times as large 
as the sun1 and  would give #ac4h times 
more light2 but many of the fixed stars 
must be  immensely greater than ,sirius4
 ,sometimes stars have all at once      
appeared1 shone with a brilliant light1 
and then vanished4 ,in #aegb a  star was
 discovered in ,cassiopeia1 which       
rapidly increased in brightness  till it
 even surpassed that of ,jupiter2 it    
then gradually diminished in  splendour1
 and after exhibiting all the variety of
 tints that indicates  the changes of   
combustion1 vanished sixteen months     
after its discovery1  without altering  
its position4 ,it is impossible to      
imagine any thing  more tremendous than 
a conflagration that could be visible at
 such a  distance4 ,some stars are      
periodic1 possibly from the intervention
 of  opaque bodies revolving about them1
 or from extensive spots on their       
surfaces4 ,many thousands of stars that 

seem to be only brilliant points1  when 
carefully examined are found to be in   
reality systems of two or  more suns    
revolving about a common centre4 ,these 
double and multiple  stars are extremely
 remote1 requiring the most powerful    
telescopes to  show them separately4    
,the first catalogue of double stars in 
which their places and relative         
positions are determined1 was           
accomplished by the talents and industry
  of ,sir ,william ,herschel1 to whom   
astronomy is indebted for so many       
brilliant discoveries1 and with whom    
originated the idea of their            
combination in binary and multiple      
systems1 an idea which his own          
observations had completely established1
 but which has since received           
additional confirmation from those of   
his son and ,sir ,james ,south1 the     
former of whom1 as well as ,professor   
,struve of ,dorpat1 have added many     
thousands to their numbers4 ,the motions
 of revolution round a common  centre of

 many have been clearly established1 and
 their periods  determined with         
considerable accuracy4 ,some have       
already since their  first discovery    
accomplished nearly a whole revolution1 
and one1 if the  latest observations can
 be depended on1 is actually            
considerably  advanced in its second    
period4 ,these interesting systems thus 
present a  species of sidereal          
chronometer1 by which the chronology of 
the heavens  will be marked out to      
future ages by epochs of their own1     
liable to no  fluctuations from         
planetary disturbances such as obtain in
 our system4    ,possibly among the     
multitudes of small stars1 whether      
double or  insulated1 some may be found 
near enough to exhibit distinct         
parallactic  motions1 or perhaps        
something approaching to planetary      
motion1 which may  prove that solar     
attraction is not confined to our       
system1 or may lead  to the discovery of
 the proper motion of the sun4 ,the     

double stars are  of various hues1 but  
most frequently exhibit the contrasted  
colours4 ,the  large star is generally  
yellow1 orange1 or red2 and the small   
star blue1  purple1 or green4 ,sometimes
 a white star is combined with a blue or
  purple1 and more rarely a red and     
white are united4 ,in many cases1 these 
appearances are due to the influences of
 contrast on our judgment of  colours4  
,for example1 in observing a double star
 where the large one is  of a full ruby 
red1 or almost blood colour1 and the    
small one a fine  green1 the latter lost
 its colour when the former was hid by  
the cross  wires of the telescope4 ,but 
there are a vast number of instances    
where  the colours are too strongly     
marked to be merely imaginary4 ,mr4     
,herschel  observes in one of his papers
 in the ,philosophical ,transactions1 as
 a  very remarkable fact1 that although 
red single stars are common enough1  no 
example of an insulated blue1 green1 or 
purple one has as yet been  produced4   

,in some parts of the heavens1 the stars
 are so near together as to form        
clusters1 which to the unassisted eye   
appear like thin white clouds2  such is 
the milky way1 which has its brightness 
from the diffused light  of myriads of  
stars4 ,many of these clouds1 however1  
are never resolved  into separate stars1
 even by the highest magnifying powers4 
,this  nebulous matter exists in vast   
abundance in space4 ,no fewer than #bejj
  nebul were observed by ,sir ,william  
,herschel1 whose places have been       
computed from his observations1 reduced 
to a common epoch1 and arranged  into a 
catalogue in order of right ascension by
 his sister ,miss ,caroline  ,herschel1 
a lady so justly celebrated for         
astronomical knowledge and  discovery4  
,the nature and use of this matter      
scattered over the heavens  in such a   
variety of forms is involved in the     
greatest obscurity4 ,that  it is a      
self-luminous1 phosphorescent material  
substance1 in a highly  dilated or      

gaseous state1 but gradually subsiding  
by the mutual  gravitation of its       
particles into stars and sidereal       
systems1 is the  hypothesis which seems 
to be most generally received2 but the  
only way  that any real knowledge on    
this mysterious subject can be obtained1
 is  by the determination of the form1  
place1 and present state of each        
individual nebula1 and a comparison of  
these with future observations  will    
show generations to come the changes    
that may now be going on in  these      
rudiments of future systems4 ,with this 
view1 ,mr4 ,herschel is now  engaged in 
the difficult and laborious             
investigation1 which is  understood to  
be nearly approaching its completion1   
and the results of  which we may        
therefore hope ere long to see made     
public4 ,the most  conspicuous of these 
appearances are found in ,orion1 and in 
the girdle  of ,andromeda4 ,it is       
probable that light must be millions of 
years  travelling to the earth from some

 of the nebul4    ,so numerous are the  
objects which meet our view in the      
heavens1 that we  cannot imagine a part 
of space where some light would not     
strike the  eye3 but as the fixed stars 
would not be visible at such distances1 
if  they did not shine by their own     
light1 it is reasonable to infer that   
they are suns2 and if so1 they are in   
all probability attended by  systems of 
opaque bodies1 revolving about them as  
the planets do about  ours4 ,but        
although there be no proof that planets 
not seen by us revolve  about these     
remote suns1 certain it is1 that there  
are many invisible  bodies wandering in 
space1 which1 occasionally coming within
 the sphere  of the earth's attraction1 
are ignited by the velocity with which  
they  pass through the atmosphere1 and  
are precipitated with great violence on 
the earth4 ,the obliquity of the descent
 of meteorites1 the peculiar  matter of 
which they are composed1 and the        
explosion with which their  fall is     

invariably accompanied1 show that they  
are foreign to our  planet4 ,luminous   
spots altogether independent of the     
phases have  occasionally appeared on   
the dark part of the moon1 which have   
been  ascribed to the light arising from
 the eruption of volcanoes2 whence it   
has been supposed that meteorites have  
been projected from the moon by  the    
impetus of volcanic eruption2 it has    
even been computed1 that if a  stone    
were projected from the moon in a       
vertical line1 and with an  initial     
velocity of #ajiib feet in a second1    
which is more than four  times the      
velocity of a ball when first discharged
 from a cannon1  instead of falling back
 to the moon by the attraction of       
gravity1 it  would come within the      
sphere of the earth's attraction1 and   
revolve  about it like a satellite4     
,these bodies1 impelled either by the   
direction of the primitive impulse1 or  
by the disturbing action of the  sun1   
might ultimately penetrate the earth's  

atmosphere1 and arrive at  its surface4 
,but from whatever source meteoric      
stones may come1 it seems  highly       
probable1 that they have a common       
origin1 from the uniformity1 we  may    
almost say identity1 of their chemical  
composition4    ,the known quantity of  
matter bears a very small proportion to 
the  immensity of space4 ,large as the  
bodies are1 the distances that separate 
them are immeasurably greater2 but as   
design is manifest in every part  of    
creation1 it is probable that if the    
various systems in the universe  had    
been nearer to one another1 their mutual
 disturbances would have  been          
inconsistent with the harmony and       
stability of the whole4 ,it is  clear   
that space is not pervaded by           
atmospheric air1 since its  resistance  
would long ere this have destroyed the  
velocity of the  planets2 neither can we
 affirm it to be void1 when it is       
traversed in  all directions by light1  
heat1 gravitation1 and possibly by      

influences  of which we can form no     
idea2 but whether it be replete with an 
ethereal  medium1 time alone will show4 
,though totally ignorant of the laws    
which obtain in the more distant        
regions of creation1 we are assured1    
that one alone regulates the  motions of
 our own system2 and as general laws    
form the ultimate object  of            
philosophical research1 we cannot       
conclude these remarks without          
considering the nature of that          
extraordinary power1 whose effects we   
have been endeavouring to trace through 
some of their mazes4 ,it was at  one    
time imagined1 that the acceleration in 
the moon's mean motion was  occasioned  
by the successive transmission of the   
gravitating force2 but  it has been     
proved1 that1 in order to produce this  
effect1 its velocity  must be about     
fifty millions of times greater than    
that of light1 which  flies at the rate 
of #bjjjjj miles in a second2 its action
 even at the  distance of the sun may   

therefore be regarded as instantaneous2 
yet so  remote are the nearest of the   
fixed stars1 that it may be doubted     
whether the sun has any sensible        
influence on them4    ,the analytical   
expression for the gravitating force is 
a straight line2  the curves in which   
the celestial bodies move by the force  
of  gravitation are only lines of the   
second order2 the attraction of         
spheroids according to any other law    
would be much more complicated2 and  as 
it is easy to prove that matter might   
have been moved according to an         
infinite variety of laws1 it may be     
concluded1 that gravitation must  have  
been selected by ,divine wisdom out of  
an infinity of other laws1  its being   
the most simple1 and that which gives   
the greatest stability  to the celestial
 motions4    ,it is a singular result of
 the simplicity of the laws of nature1  
which  admit only of the observation and
 comparison of ratios1 that the         
gravitation and theory of the motions of

 the celestial bodies are  independent  
of their absolute magnitudes and        
distances2 consequently if  all the     
bodies in the solar system1 their mutual
 distances1 and their  velocities1 were 
to diminish proportionally1 they would  
describe curves  in all respect similar 
to those in which they now move2 and the
 system  might be successively reduced  
to the smallest sensible dimensions1 and
  still exhibit the same appearances4   
,experience shows that a very  different
 law of attraction prevails when the    
particles of matter are  placed within  
inappreciable distances from each other1
 as in chemical  and capillary          
attractions1 and the attraction of      
cohesion2 whether it be  a modification 
of gravity1 or that some new and unknown
 power comes into  action1 does not     
appear2 but as a change in the law of   
the force takes  place at one end of the
 scale1 it is possible that gravitation 
may not  remain the same at the immense 
distance of the fixed stars4 ,perhaps   

the  day may come when even gravitation1
 no longer regarded as an ultimate      
principle1 may be resolved into a yet   
more general cause1 embracing  every law
 that regulates the material world4     
,the action of the gravitating force is 
not impeded by the intervention  even of
 the densest substances4 ,if the        
attraction of the sun for the  centre of
 the earthy and for the hemisphere      
diametrically opposite to  him1 was     
diminished by a difficulty in           
penetrating the interposed  matter1 the 
tides would be more obviously affected4 
,its attraction is  the same also1      
whatever the substances of the celestial
 bodies may be1  for if the action of   
the sun on the earth differed by a      
millionth part  from his action on the  
moon1 the difference would occasion a   
variation  in the sun's parallax        
amounting to several seconds1 which is  
proved to  be impossible by the         
agreement of theory with observation4   
,thus all  matter is pervious to        

gravitation1 and is equally attracted by
 it4    ,as far as human knowledge goes1
 the intensity of gravitation1 has never
  varied within the limits of the solar 
system2 nor does even analogy lead  us  
to expect that it should2 on the        
contrary1 there is every reason to  be  
assured1 that the great laws of the     
universe are immutable like their       
,author4 ,not only the sun and planets1 
but the minutest particles in all  the  
varieties of their attractions and      
repulsions1 nay even the  imponderable  
matter of the electric1 galvanic1 and   
magnetic fluids are  obedient to        
permanent laws1 though we may not be    
able in every case to  resolve their    
phenomena into general principles4 ,nor 
can we suppose the  structure of the    
globe alone to be exempt from the       
universal fiat1  though ages may pass   
before the changes it has undergone1 or 
that are  now in progress1 can be       
referred to existing causes with the    
same  certainty with which the motions  

of the planets and all their secular    
variations are referable to the law of  
gravitation4 ,the traces of  extreme    
antiquity perpetually occurring to the  
geologist1 give that  information as to 
the origin of things which we in vain   
look for in the  other parts of the     
universe4 ,they date the beginning of   
time2 since  there is every reason to   
believe1 that the formation of the earth
 was  contemporaneous with that of the  
rest of the planets2 but they show that 
creation is the work of ,him with whom  
'a thousand years are as one day1  and  
one day as a thousand years4'