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Bdifiburgk^ . • Edmonston &* Douglas. 
Dublin^ . . ,1V.//. Smith &* Son. 

bRCBMBER 9, 1874. 



In 1874. 








ISU. A. 60. 



According to the science of modem 
astronomy, the Sun occupies the centre 
of the planetary system, and the Earth 
is a planet, revolving round the Sun like 
the other planets of the system; on the 
other hand, the innumerable stars are 
supposed to be situated in space at a 
remote distance apart from the planetary 
system. But the Earth is a round body 
several thousand miles in diameter. We 
may therefore reasonably infer that the 
other planets are similarly bodies of vast 
dimensions, and this conclusion appUes 
with still greater force to the Sun, the 
central body of the planetary system. 
Furthermore, the theory of modem 


astronomy, which places the Sun in the 
centre of the planetary system, assigns to 
the stars of the celestial vault the rtle 
of so many resplendent suns, each con- 
stituting the centre of a retinue of re- 
volving bodies. In like manner, then, 
as we are led to suppose that the Sun 
is a body of great magnitude, so we 
infer, by a similar train of reasoning, 
that the stars are also bodies of vast 

But in order to ascertain the magni^ 
tudes of the celestial bodies, we must 
know their distances from the Earth. 
We are thus led to consider the supreme 
importance of the astronomical problem 


which is to form the groundwork of our 
explanations. When we have once made 
some progress in a knowledge of the 
distances of the celestial bodies, we are 
in a position to form a conception of 
the amazing extent of the physical 
universe. We thus come to learn that 
the Sun is a stupendous globe more 
than 800,000 miles in diameter, and 
that its distance from the Earth is more 
than ninety-one millions of miles. We 
learn, furthermore, that the planets are 
bodies of immense size revolving round 
the Sun, that the extreme planet of the 
system, the planet Neptune, revolves at a 
distance of two thousand eight hundred 


millions of miles from the central body, 
and that the orbits of many comets ex- 
tend even much farther into space. 
Finally, we arrive at the conclusion that 
the stars are in reality suns, exceeding 
in many instances the great central body 
of the planetary system in magnitude, 
and traversing space at an almost incon- 
ceivable distance from the Earth. 

Beaearches of the Ancient Astronomers on the 
Distances of the Celestial Bodies, 

The Greek astronomers made some in- 
genious attempts to determine the distance 
of the Sun from the Earth, but in no case 
was either the method of solution or the 


existing state of astronomy adequate to 
meet the requirements of a problem of 
such difficulty. In the case of the Moon 
they were more successful. The method 
employed by them was exactly the same 
in principle as that used by modem astro- 
nomers, and forms indeed the basis of all 
researches having for their object the 
determination of the distances of the 
celestial bodies from the Earth. A brief 
explanation of it will presently be 



Relation between the Mean Distances of the 
Planets from the Sun, and their Times of 
Revolution round that Body. 

It is a remarkable fact that although the 
ancient astronomers made no progress in the 
determination of the absolute distances ot 
the celestial bodies from the Earth, with the 
single exception of the Moon, they arrived 
at a very approximate estimate of the 
relative distances of the planets from the 
Sun. Ptolemy, who is, next to Hippar- 
chus, the greatest astronomer of antiquity, 
has given a statement of the relative dis- 
tances of the planets in a very important 
work which he has written on the science of 
astronomy; and those results, after receiv- 



ing a correction derived from the observa- 
tions of the Danish astronomer, Tycho 
Brah^, were instrumental in conducting 

Kg. 1. 

the renowned astronomer Kepler to one 
of the greatest discoveries recorded in 
the annals of science. Fig. 1 shows how 


the relative distances of Venus and the * 
Earth from the Sun may be readily 
derived from observation. S represents 
the Sun, E the Earth, and V Venus. The 
time chosen for the observation is that 
at which the angular distance of the planet 
from the Sun is the greatest possible. The 
angle SVE being then a right angle, it 
suffices to determine by observation the 
magnitude of the angle SEV in order to 
ascertain the proportion of SE to SV, 
which gives the relative distances of the 
Earth and planet from the Sun. 

With the view of enabling the reader 
to form an idea of the importance of the 
discovery of Kepler above alluded to/ we 


shall now lay before him a statement of 
the times of revolution of the eight prin- 
cipal planets, and their relative distances 
from the Sun, as derived from the most 
recent researches : — 

Time of Mean 

Bevolution. Distance. 

Mercury, 0-241 0-388 

Yenus, 0-615 0-723 

The Earth, .... 1-000 1-000 

Mars, 1-884 1-524 

Jupiter, ..... 11-868 5-203 

Saturn, 29-456 9-539 

Uranus, ..... 84-014 19-182 

Neptune, 164-610 30-037 

It will be readily seen from this table 
that, as the time of revolution of a planet 
increases, its mean distance from the Sun 


increases also. It is manifest, however, 
that the mean distance increases in a 
much slower proportion than the time of 
revolution. Thus, while the time of revo- 
lution of the planet Neptune exceeds 
the time of revolution of the Earth in 
the proportion of 164 to 1, the mean 
distance of Neptune exceeds the mean 
distance of the Earth only in the pro- 
portion of 30 to 1. It was reserved 
for Kepler to discover a relation be- ^ 
tween the times of revolution and the 
mean distances of the planets, by means 
of which one of these elements can be 
readily ascertained from a knowledge 
of the other. This theorem is generally 


called Kepler's third law of the planetary 
movements. It may be thus enunciated : 
— The squares of the times of revolution 
of the playlets are proportional to the 
cubes of their mean distcmces from the 
Sun. The significance of this law will 
be readily understood by a reference 
to the foregoing table. Thus, to take 
the case of the planet Mars — ^its time of 
revolution is 1*884, the square of which 
is 3*53 ; again, its mean distance is 
1*524, the cube of which is 3'53, a result 
exactly equal to the square of the time 
of revolution. In the same way, if we 
take any other planet, and if we square 
the time of revolution and cube the 


mean distance, we shall obtain two sets, 
of numbers which will be identical, or 
very nearly identical, with each other. 
Furthermore, it is plain from this law 
that, if we know the time of revolution 
of a planet, we have only to square it, 
and we obtain a result, the cube root of 
which wiU give the mean distance of the 
planet from the Sun. Conversely, if we 
know the mean distance, we have only to 
form the cube of it, and the square root 
of the result will give the time of 

It is important to bear in mind that 
in the table which we have given repre- 
senting the times of revolution and mean 


distances from the Sun of the principal 
planets, it is only the relative distances 
which are set down. Thus we learn from 
the table that the mean distance of Jupiter 
is 5*203 — the Earth's mean distance being 
represented by unity ; but the table gives 
us no information respecting the absolute 
value of this unit. It is clear, however, 
that if we assign a certain numerical 
value to it, we are then in a position to 
determine the absolute numerical value of 
the mean distance of any planet, from 
the sun. Thus, if the unit be expressed 
by ninety-one and a half milHons of 
miles, this number will then represent 
the absolute mean distance of the Earth 


from the Sun; and similarly the mean 
distance of Jupiter, as given in the 
table, upon being multiplied by ninety- 
one and a half millions of miles, will 
give, in round numbers, four hundred 
and seventy-six millions of miles as 
the absolute mean distance of the 
planet from the Sun. We thus learn the 
supreme importance of ascertaining the 
absolute mean distance of any one planet 
from the Sun ; for this object being once 
achieved, the mean distances of all the 
other planets from the Sun may be readily 
computed by an arithmetical process, either 
from the table of relative distances, or 
by means of Kepler's third law. 


Eayplanation of the Method for Fivding the 
Distance of an Inaccessible Object 

The determination of the distance of an 
inaccessible object appears to many per- 
sons to be an undertaking of insuperable 
difficulty. Nothing can be more simple 
than the principle which underlies the 
solution of this problem. Let A represent 
the position of an observer who wishes 
to ascertain his distance from an inac- 
cessible object O. He first carefully 
measures the distance between the station 
A and another station B. The line thus 
measured is called a hose line. With a 
theodolite he then measures the bearing 



of O relatively to the station B. He next 



proceeds to the station B, and similarly 

measures the bearing of O with respect 



to the station A. In this manner 
he determines the two angles at the 
base of the triangle AOB, and having 
already ascertained by measurement the 
length of the base AB, he is in a posi- 
tion to compute the remaining sides and 
angles of the triangle. He thus arrives 
at a knowledge of the lengths of the 
lines AO, BO, which represent the dis- 
tance of the object from each of the 
two stations. 

In Fig. 2, the letters S, E, N, W, 
denote the cardinal points of the horizon, 
South, East, North, West. Now it is 
clear that when the object O is viewed 
from A, it appears in the direction north- 


east ; on the other hand, when observed 
from B, it appears in the direction north- 
west. The angle AOB, formed by the 
lines AO, BO, indicates therefore the 
change of direction which the object under- 
goes in consequence of the observer shift- 
ing his position from A to B. It has 
received an important designation. It is 
called the parallax of the object. 

Difficulty experienced in Applyi/ng the fore- 
going Principle to the Celestial Bodies, 

In endeavouring to ascertain the dis- 
tances of the celestial bodies by the ap- 
plication of the principle explained above, 
we at once encounter a grave diflficulty. 



Fig. 3. 


B A- 



In Fig. 3, let S, S, S, represent a 
celestial body at diflferent distances from 
a base line AB of invariahle length. 
The parallax of the object is obviously 
represented by the angle SBC, formed 
by drawing BC parallel to AS. Now, 
it is clear, by an inspection of the figure, 
that the more distant the object is, the 
smaller does the angle of parallax be- 
come, insomuch that finally the distance 
of S may be so great that the line drawn 
parallel to AS coincides sensibly with 
BS, and the angle of parallax vanishes 
altogether. Now, if we fail to determine 
the angle at S, which represents the par- 
allax of the object, we have no means 


of solving the triangle ASB, and con- 
sequently we are unable to ascertain the 
value of the distance AS or BS. 

We have hitherto supposed the base 
line to be invariable. Let us now con- 
sider what would be the effect produced 
by assigning to the base line a variable 
length, and placing the celestial object S 
at the same constant distance. It is 
manifest, by referring to Fig. 4, that 
as the ba^e Une diminishes the angle 
of parallax diminishes also, insomuch 
that finally we may imagine S to be so 
remote that the line BC, drawn par- 
allel to AS, coincides sensibly with BS, and 
the angle of parallax vanishes altogether. 



We now perceive clearly the main source 

Fig. 4. 

of the difficulty experienced in determin- 
ing the distances of the celestial bodies 


from the Earth. It arises in the first 
place from the extreme remoteness of 
those bodies, and secondly from the com- 
parative smallness of the base from which 
they are measured. The Earth is a body 
of only eight thousand miles in diameter ; 
consequently any base line drawn on its 
surface cannot possibly exceed a few 
thousand miles in length. This, however, 
is an insignificant magnitude compared 
with the immense distance of the celes- 
tial bodies. In consequence of this cir- 
cumstance the parallax of a celestial 
object is so excessively small that, imtil 
towards the close of the seventeenth 
century, its determination even approx- 


imately in any case, with the single 
exception of the Moon, had steadily 
continued to baffle the eflforts of 

In observing the celestial bodies, it is 
usual for astronomers to refer their ap- 
parent positions to the centre of the Earth 
which is the true physical centre of the 
terrestrial globe. Indeed, since the Earth 
is a body of considerable dimensions, it 
is plain that observations made from 
different places on its surface could not 
be comparable unless they were referred 
to some common centre. In Fig. 5 let 
P, P', be two celestial bodies ; A the 
position of an observer on the Earth's 



surface, and let C denote the centre of 
the Earth. P is supposed to be in the 
zenith ; consequently P ' is supposed to be 

Fig. 6. 

removed from the zenith by the angle 
PAP'. Now, the object P being in the 
zenith, occupies the same apparent posi- 
tion when viewed from A, as it would 


do if seen from the centre of the 
Earth. The object P', on the other 
hand, when viewed from A, is dis- 
placed relatively to the Earth's centre 
by the angle AP^C. This angle is called 
the diurnal parallax of the object. While 
the parallax vanishes for an object in the 
zenith, it attains its maximum value for 
an object which is in the horizon, as 

Fig. 6. 

in Fig. 6, which exhibits the horizontal 
parallax P, namely, the angle APC. 


It appears then that, in order to deter- 
mine the distance of a celestial body from 
the Earth, two things are necessary. First, 
we must know the exact length of the 
base line from which the observations of 
the object are made ; secondly, we must 
detect an appreciable parallax of the 
object depending upon the observations 
made at the two extremities of the base. 
As regards the base line, we are enabled 
to compute its length exactly when we 
once know the magnitude and figure of 
the Earth, and the longitude and latitude 
of each of the two extremities of the 
base. The measurement of the angle of 
parallax is manifestly an operation of 


much delicacy, in consequence of its ex- 
treme minuteness ; for, except under ex- 
ceptionally favourable circumstances, it 
eludes the eflforts of the most skilful 

It has been already stated that, if 
we once ascertained the absolute dis- 
tance of any one of the planets from 
the Sun, the table of relative distances 
would enable us to compute the absolute 
distances of all the others/ Now, the 
Earth bemg a planet, it is clear that we 
could eflfect this important object if we 
succeeded in determining the exact value 
of the solar parallax. We now begin to 
perceive the immense magnitude of the 



results derivable from a knowledge of 
this element. 

To ascertain tlie value of the solar 
parallax by direct observations of the Sun 
has been found impracticable for various 
reasons, which it would be out of place 
to attempt explaining here. Instead of 
attacking the problem in this way, a;Stro- 
nomers have skilfully evaded its more 
formidable difficulties by deducing the 
value of the solar parallax from obser- 
vations of certain of the planets. It is 
clear from what has been already stated 
that the nearer a planet is to the Earth 
the more favourable are the circumstances 
for the determination of its parallax. 


Now, there are two planets which occa- 
sionally approach comparatively near to 
the Earth. These are the planets Venus 
and Mars — ^the one revolving immediately 
within the Earth's orbit, the other re- 
volving immediately beyond it. We 
shall commence with a remark or two 
on Mars, which was the planet first em- 
ployed for determining the solar paral- 

Fig. 7 represents the orbits of the 
Earth and Mars, on the supposition that 
they are both circles, having the Sun in 
their common centre S. Let the Earth 
be travelling in its orbit at E ; join SE, 
and imagine it to be extended so as 




to meet the orbit of Mars in M. Now 
it is plain that when the planet is 

Fig. 7. 

at M, it is nearer to the Earth (sup- 
posed for the sake of explanation to be 
always at E) than when it is in any 
other part of its orbit. In this position 


the planet is technically said to be in 
opposition, the reason being that when 
viewed from the Earth it then appears 
in the opposite region of the heavens 
to that in which the Sun is situate. Thus, 
if at the time when the planet is in opposi- 
tion it is midnight, the Sun being then 
due north and under the horizon, the 
planet will appear due south and above 
the horizon. It is obvious therefore that 
when the planet is in opposition it is 
much nearer to the Earth than when it 
is in any other part of its orbit. But 
in point of fact the circumstances are 
much more favourable than we have 
imagined. We have assumed that the 



orbits of the Earth and the planet are 
both circles. In reality, however, they 
are ellipse^. The orbit of Mars is con- 
siderably excentric; that of the Earth is 
less so : but the two orbits are so placed 
relatively to each that their excentricities 
combine together in producing occasionally 
a comparatively near approach of the 
two planets. Thus, when the planet is 
in the 'perihelion^ and consequently in 
the position where it is nearest posdhle 
to the Sun, and if it be at the same time 
in opposition, the Earth will be very near 
the aphelion of its orbit, and consequently 
will be the farthest possible from the 
Sun. In this position then the planet 


will as it were retire (within its supposed 
circular orbit) to meet the Earth, while 
the Earth will advance outwards (beyond 
its supposed circular orbit) to meet the 
planet. The consequence of this favour- 
able state of matters is that, while in 
general the distance between the Earth 
and planet at the time of opposition 
amounts to fifty or sixty milUons of 
miles, it occasionally diminishes so as 
not to exceed thirty-five millions of miles. 
This near approach of the two planets 
happens at intervals of fifteen or seven- 
teen years. It was first taken advantage 
of for determining the solar parallax in the 
seventeenth century by Cassini, an eminent 


French astronomer, who obtained 9"*5 
for the value of the solar parallax, whence 
the distance of the Sun from the Earth 
would be eighty-five millions of miles. 
This method of determining the Sun's 
distance from the Earth has been used 
on several subsequent occasions. 

But the planet Venus furnishes a 
method ' of a peculiar kind for ascertain- 
ing the value of the solar parallax^ 
which has been considered to be more 
entitled to confidence than any other 

method heretofore employed for the pur- 
pose. This beautiful planet, as has been 
already stated, revolves immediately with- 
in the Earth's orbit. Fig. 8 gives a 



graphic representation of the various 
positions which it assumes as it revolves 

round the Sun, the Earth being assumed, 
for the sake of illustration, to be station- 


ary at E. When the planet is at '^y it 
is then immediately beyond the Sun, and 
the Earth, Sun, and planet are in the 
same straight line. In this position the 
planet is said to be in superior conjunc- 
tion. The illuminated hemisphere being 
turned wholly towards the Earth, the 
planet, if it were possible to see it, would 
present a round disc, like the full Moon. 
It is, however, immersed in the efiulgence 
of the Sun's light, and is consequently 
invisible. In this position both Sun and 
planet rise and set together. As the 
planet revolves in its orbit, the illumi- 
nated hemisphere is gradually turned 
away from the Earth, and the planet as- 


sumes a gibbous aspect, as at ^; it also 
now begins to set after the Sun, and is 
therefore an evening star. At "ifi it as- 
sumes the appearance of the half moon ; 
the time of its visibility above the hori- 
zon after sunset is also now the longest 
possible. In this position the planet 
is said to be at its greatest eastern 
elongation. After quitting this position 
the planet assumes the form of a beau- 
tiful crescent, as at v^; it also now 
gradually approaches the Sun, continuing 
a shorter time above the horizon on each 
successive night. When the planet ar- 
rives at 1;^ the Sun, Earth, and planet 
are again in the same straight line. The 


planet is now said to be in inferior con- 
junction. In this position it comes di- 
rectly between the Sun and the Earth. 
The Sun and the planet now rise and set 
together. When the planet has advanced 
beyond this position it rises and sets 
before the Sun, and is, consequently, now 
a morniiig star; and the same succession 
of phases is reproduced in a reverse 
order, until the planet finally arrives in 
superior conjunction at v^, when both Sun 
and planet again rise and set together. 

Now, it is clear from this explanation that 
when the planet is in inferior conjunction, it 
is nearer to the Earth than in any other 
part of its orbit. The occasion is there- 


fore especially favourable for the determi- 
nation of its parallax. But, unfortunately, 
the same cause which prevents the planet 
from being generally visible, when it is 
in superior conjunction, is equally efficacious 
in this case also. There are, however, 
certain rare occasions when the planet 
may be seen in this position, not however 
as a star, but as a ovund black spot passing 
over the Sun's disc. Since Mercury and 
Venus both revolve within the Earth's 
orbit, they may occasionally be seen in 
this manner between the Earth and the 
Sun. A phenomenon of this kind is 
technically termed a transit of the planet. 
The importance of the transits of Venus 


over the Sun's disc for ascertaining the 
value of the solar parallax was first pointed 
out by James Gregory, and was after- 
wards insisted upon more fully by Halley. 
In 1761 and 1769 there occurred transits 
of Venus over the Sun's disc, and in 
both cases, the occasion was deemed to be 
of so great importance that the principal 
nations of Europe despatched observers 
to various parts of the world for the pur- 
pose of observing the phenomenon. 

The phenomenon to be observed may 
be readily understood by reference to 
Figure 9. The large circle represents 
the Sun. The smaller circle represents 
the planet. The planet enters upon the 


Sun^s disc, making exterior contact with 
it at 1, and interior contact at 2. It 

then travels along and leaves the solar 
disc on the right, making interior contact 
with the solar limb at 5, and exterior 
contact at 6. The object of the observer 
is especially to note the precise instant 



when the planet makes interior contact 
with the Sun's limb as at 2 and 5. 

Two methods of determining the solar 
parallax, on the basis of observations of 
the transit of Venus over the Sun's disc, 
have been devised by astronomers. The 

Fig. 10. 

earliest of these methods was that pro- 
posed by Halley. It may be thus 
explained: — ^Let E, E' be two places of 
observation in opposite parts of the 
Earth, the one being near the north pole, 


and the other near the south pole. An 
observer at the centre of the Earth would 
see the planet travel along the dotted 
chord included between the chords OP, 
QR. The observer at E sees the 
planet describe upon the Sun's disc the 
chord QR. The observer at E' sees 
the planet describe the chord OP. 
Now, the difference between the times 
of describing the two chords QR, 
OP, constitutes an indication of the 
displacement in the path of the planet 
resulting from the difference in position 
between the two stations of observation 
E, E'. But this displacement depends 
upon the absolute distance of Venus and 



the Earth from the Sun. By means, 
therefore, of the duration of the transit 
of Venus as observed from two distant 
stations on the Earth's surface, an indi- 
cation is obtained of the value of the 
solar parallax, and consequently of the 
Sun's distance from the Earth. 

The other method of determining the 
solar parallax by observations of the 
transit of Venus, is founded upon observ- 
ing the internal contact of the planet with 
the sun at two distant stations on the 
Earth's surface. Thus, let E, E', be two 
such stations ; the observer at E sees the 
ingress of the planet upon the Sun's disc 
when it arrives at a; on the other hand, 


the observer at E' does not see the 

ingress of the planet until it arrives at 6. 

The interval of time which the planet 

Fig. 11. 

thus occupies in passing from a to 6 
constitutes the groundwork of the solution 
of the problem for finding by this method 
the Sun's distance from the Earth. 

The problem may be solved in a similar 
w^y l>y observations made, at two distant 
stations, of the egress of the • planet from 
the Sun's disc. In this case the interval 


of time, which the planet occupies in 
describing the arc cc2, as observed at 
EE', supplies an indication of the Sun's 
distance from the Earth. This is tenned 
Dehsle's method, because it was first 
suggested by Delisle, a French astro- 
nomer, in contradistinction to the method 
based upon the observed duration of the 
planet on the Sun's disc, which is due to 

The method of Delisle requires a 
comparison of the exax^t times of ingress 
or egress of the planet, as observed at 
the two stations. To effect this object 
we must determine the longitudes of 
the stations relatively to Greenwich or 


some known meridian. This is in all 
cases an operation of much delicacy. 

Careful preparations were made to 
observe the transit of Venus, which 
occurred in 1761 ; but the weather was 
generally unfavourable for the purpose. 
Stm more systematic and extensive 
arrangements were made to observe 
the transit of 1769. In this instance 
the operations were successful, the 
phenomenon having been satisfactorily 
observed by a great number of persons 
in different parts of the world. In 
1824, the totality of the observations 
of the transits of 1761 and 1769 
were submitted to a profound discussion 




by the celebrated German astronomer, 
Encke, who deduced from them a 
parallax mdicating the Sun's distance 
from the Earth to be, in round num- 
bers, ninety-five millions of milea This 
result was speedily adopted by astro- 
nomers, and continued to be inserted 
in all text-books on astronomy until 
quite a recent period. It is now ascer- 
tained beyond all doubt that the value of 
the solar parallax assigned by the German 
astronomer is considerably erroneous. 

If the planet Venus revolved in the 
plane of the ecliptic, it would be seen as 
a round spot passing over the Sun's disc 
every time it arrived in inferior conjuno- 


tion. But, in point of fact, the orbit of 
the planet is inclined to the plane of 
the Earth's orbit, and the result conse- 
quently is that the planet can be seen 
on the Sun only when, at the time of 
inferior conjunction, it is passing through, 
or very near, either of the nodes of its 
orbit. Let us suppose two hoops, one 
of which is a little larger than the 
other. Let them both have a common 
centre, and let them be inclined to each 
other at a given angle. Further, while 
the Sun is supposed to be in the common 
centre of the hoops, let us assume that 
Venus revolves in the inner, and the 
Earth in the outer, hoop. Let a 



common diameter of the two hoops be 
drawn through the points where the 
inner hoop intersects the plane of the 
outer hoop. The points here referred 
to represent the nodes of the planet's 
orbit, and the diametral line pass- 
ing through them is called the line of 
nodes. A transit of the planet can 
happen only in June or December, 
because the Earth can only then be 
situated in the line of nodes of the 
planet's orbit. When the planet is pass- 
ing through its ascending node, the 
transit happens in December ; when it 
is passing through the descending node, 
the transit necessaxUy occurs in June. 


Transits generally occur at intervals of 
105^ years, 8 years, 121^ years, 8 years, 
105^ years, 8 years, &c. Frequently, 
however, instead of the transits occurring 
in pairs, there may be only one transit 
and then a long interval of more than a 
hundred years. The recurrence of transits 
at intervals of only eight years arises 
from the fact that thirteen revolutions of 
the planet are eflfected in almost exactly 
the same time as eight revolutions of 
the Earth; consequently, if the planet 
should be in either of the nodes of its 
orbit at the time of inferior conjunction, 
it will be very nearly in the node after 
the lapse of eight years, sufficiently near> 


perhaps, to bring about another transii 
of the planet. If the planet shoulc 
pass OTer the Sun's disc very near th« 
centre, its displacement after the lapsi 
of eight years may be too great to alloT 
of another transit. 

Earrlier Transits of Venue. 

The earhest prediction of a transit o 
Venus over the Sun's disc is due t" 
Kepler, In 1629 he announced tha 
a transit of the planet would occu 
in 1631. "When the time asaignei 
for the occurrence of the phenomeno] 
finally arrived, astronomers searched fo 
the planet on the Sun's disc, but withou 


success. It is now known that the 
transit really did occur, but that the 
planet passed over the Sun's disc in 
the night time, and was consequently 
invisible to the astronomers of Europe. 
Another transit of Venus occurred in 
1639. The phenomenon appears to 
have wholly escaped the attention 
of astronomers on this occasion, with 
the exception of two young English- 
men, Jeremiah Horrocks and William 
Crabtree, who alone had the privi- 
lege of witnessing a spectacle, the like 

of which no mortal had hitherto 
ever seen. Horrocks was curate of 
Hoole, near Preston. He was endowed 



with an original genius of a high order, 
and an ardent enthusiasm in the pursuit 
of science; and although he died in the 
very flower of his age, lie has left 
behind hun a name which wiU Uve 
imperishablj in the annals of science. 
By means of his own calculations he 
discovered to his great delight that there 
would be a transit of the planet in 
November 24 (O.S.), 1639, and he hastened 
to make suitable preparations for observ- 
ing the phenomenon. 

The plan of observation devised by 
him consisted in admitting the Sun's 
light into a dark room through an 
aperture in the window, and receiving 


the image of the Sun upon a white screen 
attached to the opposite wall. The 
transit of the planet over the Sun's disc 
would then be indicated by the presence 
of a round black spot traversing the 
white circle. 

Horrocks watched the solar image 
carefully throughout the whole of the 
23rd of November, but no trace of 
the planet was seen. On the morning 
of the 24th, which was Sunday, he simi- 
larly scrutinized the image of the solar 
disc, but failed to obtain any indication 
of the presence of the planet. After an 
absence of some time, caused by the 
necessity of attending to his clerical 



duties he repaired again with eager 
anxiety to the darkened chamber, when, 
'' Oh^ most grati^ring spectacle ! " said 
he, '^ the object of so many esunest 
wishes^ I perceived a new spot of unnsoal 
magnitude, and of a perfectly round form, 
that had just wholly entered upon the 
left limb of the Sun, so that the margin 
of the Sun and the spot coincided with 
each other, forming the angle of contacf 
Owing to the near approach of sunset, 
Horrocks was unable to observe the planet 
longer than half an hour. Crabtree, who 
resided near Manchester, had, in accord- 
ance with instructions from Horrocks, 
made similar preparations for observing 


the phenomenon, and he also enjoyed the 
gratification of seeing the planet on the 
Sun's disc; but a cloud came over the 
Sun s face, and he was unable to make 
any precise measures. The observations 
of Horrocks have furnished valuable 
materials in recent years for correcting 
the elements of the orbit of the planet. 

Horrocks, as already stated, died young, 
but he has left behind him unmistake- 
able proofs of a thoroughly original 
genius, and a capacity for the cultiva- 
tion of physical science which have 
earned for him a lasting reputation. In 
the present day, when a transit of the 
planet is close at hand, steps have been 



taken by the men of science of his 
country to erect a fitting tribute to his 
memory in Westminster Abbey. 

The Trandts of 1761 and 1769. 

It has been abready stated that the 
weather was generally unfavourable for 
the observation of the transit of 1761. 
The preparations for observing the transit 
of 1769 were upon a more extensive scale, 
and led to a more successful issue. The 
British Government despatched observers 
to Otaheite, in the Pacific Ocean, for the 
purpose of observing the phenomenon. 
The ship in which they sailed, the 
*' Endeavour," was commanded by the 


celebrated navigator, Captain James Cook. 
The other principal nations of Europe 
made similar preparations, with a view to 
the observation of the transit. The 
weather on the whole was favourable for 
the observation of the phenomenon, and 
the operations were skilfully executed. 
The method chiefly relied upon was that of 
durations, as illustrated in Fig. 10. Two 
of the most important stations were 
Otaheite, in the southern hemisphere, 
and Wardhus, in Lapland, in the northern. 
The duration of the transit at Wardhus 
was 5 hours 54 minutes ; the duration at 
Otaheite was 5 hours 32 minutes. The 
diflference of durations amounted therefore 



to 22 minutes. This interval of 22 
minutes constituted the result leading to 
the determination of the solar parallax. 
If the absolute distances of the Sun 
and the planet from the Earth were 
gradually increased (the relative distances 
of the two bodies remaining unchanged), 
the difference of duration of the transit 
would gradually diminish, until ultimately 
it would be so small as to be inappreciable. 
Now 22 minutes constitute a considerable 
interval of time for measurement, and it 
happens that a small error committed in 
its determination would entail a rela- 
tively much smaller error in the compu- 
tation of the solar parallax. 


Shortly after the occurrence of the 
transits of 1761 and 1769 various evalua- 
tions of the solar parallax were deduced 
from the resulting observations, but the 
discordances of the results thus obtained 
were greater than was deemed satisfac- 
tory. It has been already mentioned 
that Encke submitted the totality of 
the observations of both transits to a 
comprehensive discussion. The German 
astronomer obtained 8"*5776 for the 
definitive value of the solar parallax. 
This would indicate the Sun's distance 
from the Earth to be, in round numbers, 
ninety-five millions of miles. 

A difficulty of an unexpected and 


serious nature occurred to the observers 
of the transit of Venus on these occasions. 
It was found that the ingress of the planet 
on the Sun's disc was characterized bj the 
presence of a pear-shaped, dark ligament, 
connecting the planet with the Sun's limb, 
and rendering it a matter of exceeding 
difficulty to pronounce upon the precise 
instant when the two bodies formed 
internal contact. It was to the un- 
certainty of the observations arismg from 
this cause (a purely optical one) that the 
discordance between the results obtained 
for the value of the solar parallax by 
different astronomers was in a great 
measure attributable. 


Mcyre Recent Determiifiations of the Value 
of the Solar Parallax. 

The value of the Sun's distance from the 
Earth resulting from the researches of 
Encke in 1824 continued to be adopted 
in all popular treatises on astronomy as 
representing the most trustworthy value 
of that element which had hitherto been 
arrived at. In recent years, however, 
astronomers have found reason to suspect 
that the evaluation of Encke is considerably 
in error. As early as 1854, Hansen, in 
a letter to the Astronomer Royal, an- 
nounced that his researches in the lunar 
theory seemed to indicate that Encke's 



value of the solar parallax was too small 
(and consequently that the resulting dis- 
tance of the Sun from the Earth was too 
great). Subsequently, he determined in 
this manner the value of the solar parallax^ 
and he found it to be S^'SIG. Stone, the 
first Assistant at the Royal Observatory, 
Greenwich (now Her Majesty*s Astro- 
nomer at the Cape of Grood Hope), deduced 
a similar result from observations of the 
planet Mars, made in 1862, when it ap- 
proached very near to the Earth. His 
computations gave 8''*943 for the resulting 
value of the solar parallax. About the 
same time Le Verrier, the eminent French 
Astronomer, obtained S^'SSQ from his re- 


searches in the planetary theory. These 
various determinations concurred in in- 
dicating that the true distance of the Sun 
from the Earth was not ninety -five 
millions of miles, as had been hither- 
to supposed, but rather • somewhere 
about ninety-one and a half millions 
of miles, or about ^Vth less than the 
assumed value. This conclusion received 
a striking confirmation from an un- 
expected source. The velocity of light 
may be determined astronomically in 
two different ways. One of these 
is founded upon observations of the 
eclipses of Jupiter's satellites. When the 
Earth is in the part of its orbit which is 


nearest to the planet, the eclipses occur 
earlier than the predicted times. On the 
other hand, when it is in the more remote 
part of its orbit, the eclipses occur later 
than the times computed from theory. 
These discordances may all be got rid of 
by assuming that light is not propagated 
instantaneously, but, on the contrary, 
occupies some time in passing through 
space. Now, it is found in this way that 
light occupies sixteen minutes in travers- 
ing a diameter of the Earth's orbit. As- 
suming, then, that the radius of the 
Earth's orbit is ninety-five milUons of 
miles, we hence arrive at the conclusion 
that light traverses space with the amaz- 


ing velocity of one hundred and ninety- 
two thousand miles in a second. 

The other method is founded upon a 
curious phenomenon of the stars. When 
their apparent positions are carefully 
scrutinized, it is observed that the stars 
all describe a very small ellipse in the 
heavens, a fact which may be satisfactorily 
explained by assuming that light occupies 
a certain interval of time in passing from 
a star to the earth. Now, the magni- 
tude of the major axis of the ellipse 
described by a star in this case depends 
upon the proportion which the orbital 
velocity of the earth bears to the 
velocity of light. Here, then, we have 


three quantities, from any two of which we 
can derive the third — ^namely, the major 
axis of the ellipse of aberration as it is 
called, the velocity of the Earth in its 
orbit, and the velocity of light. Now, 
observations of the stars give us the 
value of the first of these three quantities, 
and if we assume the radius of the Earth's 
orbit to be ninety-five millions of miles, 
we can readily compute from it the orbital 
velocity of the Earth. Knowing then 
these two quantities, we are in a position 
to determine the third, and thus we arrive 
at the conclusion that light travels 
through space at the rate of one hundred 
and ninety-two thousand miles in a 


second, as indicated by the eclipses of 
Jupiter's satellites. 

But, wonderful to relate, the velocity 
of light has been determined by an 
experimental process, conducted upon the 
Earth's surface within the compass of a 
few^ hundred yards. This has been ac- 
complished by two distinct methods, 
both due to two French physicists, 
Fizeau and Foucault. The results ob- 
tained in the two instances agree in 
assigning to light a velocity of one 
hundred and eighty-five thousand miles 
in a second. Here, then, we have pre- 
sented to us a striking discordance 
between the value of the velocity of 


light deduced astronomicallj^ as stated 
above, and the value obtained by the 
French physicists. But in computing 
the velocity of light astronomically, we 
assumed that the radius of the Earth's 
orbit was ninety-five millions of miles. 
Let us, however, suppose the radius' of 
the orbit to be ninety-one and a half 
millions of miles, as pointed out by the 
recent researches of astronomers, and we 
obtain by both astronomical methods a 
velocity amounting to one hundred and 
eighty-five thousand miles in a second^ 
precisely the same value as that indi- 
cated by the experiments of the French 


Thus it appears that the terrestrial 
experiments for ascertaining the velocity 
of light concurred with recent astrono- 
mical researches in indicating the ne- 
cessity of adopting a larger value of 
the solar parallax than the value hitherto 
employed by astronomers. 

Finally, Stone having investigated anew 
the question, in so far as concerned the 
transit of 1769, ascertained that, by a juster 
interpretation of some of the observations 
the resulting value of the solar parallax 
agreed very nearly with the value derived 
from other sources. In fact, he found 
in this manner the value of the solar 
parallax to be 8"*91, indicating the Sun's 




distance {rom the Earth to be ninet 
million six hundred thousand mile& 

Details respecting the Transit of Venus in 

December 8, 1874. 

It has been already stated that the 
observation of the transit of Venus con- 
sists in noting the precise instant when 
the planet^ in its passage over the Sun s 
disc^ forms internal contact with the 
margm of the Sun, first at ite ingress 
upon the solar disc, and secondly, at 
its egress from the disc. If we suppose 
an observer to be situated at the centre 
of the Earth, he would see the inter- 
nal contact at ingress on the morning 


of the 9th of December at 2 h. 15 m. 
Greenwich Mean Time, and he would 
see the internal contact at egress at 
5 h. 57 m. The included interval of 
time is therefore 3 hours 42 minutes. 
But the interval of time which elapses be- 
tween the instant when the planet first 
impinges on the solar disc, and the 
instant when it finally leaves the disc is 
necessarily somewhat greater, as may be 
seen by referring to Fig. 9. It amounts, 
in fact, to 4 hours 41 minutes. An 
observer on the Earth's surface, having 
the Sun in his zenith, would see the 
different phases of the transit exactly 
as an observer at the centre of the 


Earth would see them. But the result 
would be different if he were stationed 
at any other place on the Earth's 
surface, as may be readily understood by 
referring to Figures 10 and 11. Let us 
confine our attention to the instant of 
internal contact at ingress and egress. 
Of course, the transit can only be visible 
from the illuminated hemisphere of the 
Earth ; or, in other words, the hemis- 
phere which is turned towards the Sun. 
Now, there are certain places on the 
Earth's surface from which the internal 
contact of the planet with the Sun at 
ingress may be seen earlier than it 
would be seen to an observer stationed 


at the centre of the Earth; and again, 
there are other places where the internal 
contact at ingress would be seen later 
than it would be seen from the centre 
of the Earth, Now, if the Sun had no 
sensible parallax, the time of internal 
contact, whether at ingress or egress, 
would be the same everywhere on the 
Earth's surface as at the centre. It is 
clear, then, that the difference between 
the times of internal contact at ingress 
or egress, as observed from two distant 
stations on the Earth's surface constitutes 
the datum available to the astronomer 
for the solution of the problem of the 
Sun's distance from the Earth. The 



following plan of localization as r^ards 
stations accordingly offers itself as most 
suitable for observing the phenomenon. 

1. Stations where the internal contact 
at ingress is accelerated. 

2. Stations where the internal contact 
at ingress is retarded. 

3. Stations where the internal contact 
at egress is accelerated. 

4. Stations where the internal contact 
at egress is retarded. 

It is upon this principle that astrono- 
mers have selected a great number of 
stations in various parts of the world, for 
the purpose of observing the transit. 
Let us take^ for example, Woahoo in the 



Sandwich Isles, and Kerguelen Island. 
The internal contact will be seen eleven 
minutes earlier from Woahoo, and twelve 
minutes later from Kerguelen Island than 
if it were viewed from the Earth's centre. 
Hence the interval between the times of 
internal contact, as seen at Woahoo and 
Kerguelen Island, amounts to twenty- 
three minutes. Similarly, the astronomer 
combines the observations made at two 
stations, where the internal contact at 
egress is seen earlier in the one case, and 
later in the other, than if the phenomenon 
was seen at the centre of the Earth. 



ArrangeTnenta for observing the TramsU of 

Venus in 1874. 

As early as 1857, the Astronomer 
Royal, in a paper communicated to the 
Royal Astronomical Society, drew the 
attention of astronomers to the approach- 
ing transits of Venus over the Sun's 
disc in 1874 and 1882; and on several 
subsequent occasions he explained his 
views on the subject to the Society. 
The Government having been made to 
understand the importance attached to 
the proper observation of the transit of 
1874, induced Parliament to vote a con- 
siderable sum of money for defraying the 


necessary expenses. The whole of the 
arrangements connected with the different 
expeditions for observing the pheno- 
menon have been planned and executed 
under the superintendence of Sir George 
Airy, the Astronomer Royal. Five 
stations were originally chosen for the 
observation of the transit. These were, 
Alexandria, Honolulu, Rodriguez, New 
Zealand, and Kerguelen Island. It 
was subsequently considered desirable to 
supplement the station at Honolulu 
by two additional stations at some 
distance apart. These are Hawaii and 
Kauai. An additional station has 
also been attached to Kerguelen Island, 



and one at Cairo, in connection with the 
station at Alexandria. Furthermore, two 
stations have been established in India. 
In addition to these preparations, the 
transit will not £ail to receive due 
attention at the observatories of Mel- 
bourne, Sydney, the Cape of Good Hope, 
and Madras. Some of the Colonial 
Governments of Australia have voted 
special grants of money for the observation 
of the phenomenon. Then there is the 
very complete expedition fitted out by 
Lord Lindsay, with the view of observing 
the transit at the Mauritius. Colonel 
Campbell, of Blythswood, has also under- 
taken to observe the phenomenon 


at Thebes. The various observing 
parties despatched from Greenwich have 
been furnished with an admirable 
equipment of instruments with the use 
of which the several observers have 
undergone a course of training at the 
Royal Observatory during the last two or 
three years, under the guidance of Captain 
Tupman, R.M.A. Photography will be 
used in connection with the observatories 
at all the stations. Mr. Warren De La 
Rue has liberally undertaken to superin- 
tend this part of the Greenwich arrange- 
ments. Much ability has been displayed 
by Proctor in the discussions generally 
relating to the two transits. 



The observers connected with the 
various Greenwich expeditions are chiefly 
naval officers, with the addition of some 
officers of the engineers and artillery, and 
a few private observers. The following 
plan of arrangements, relative to the 
appointment of the different observers, 
was drawn up and issued some months ago 
by the Astronomer Royal. 

Aiypointmenta of Observers to the sevefi'ctl Dis- 
tricts of Obsei^ution, and Subordination of 

"1. Captain G. L. Tupman, KM. A., 
is head of the entire enterprise, and is 
responsible, through the Astronomer 


Royal, to the Government for every part. 
Every observer is responsible to Captain 

^'2. When the different expeditions are 
separated, the observers in each district of 
observation are responsible to the local 
chief of the district, and the chief to the 
Astronomer Royal. The districts of ob- 
servation and the observers will be the 
following, the name first following that of 
the local chief being that of the deputy, 
who will, if necessary, take his place ; — 

'' 3. District A. Egypt: Chief, Capt. C. . 
O. Browne, R.A., astronomer; Observers, 
Capt. W. de W. Abney, R.E., astronomer 
and photographer; S. Hunter, astronomer. 



" 4. District B. Sandwich Islands : Gene- 
ral Chief, Capt. G. L. Tupman, R.M. A. : 
Deputy, if necessary. Prof. G. Forbes. 

" Subdivisions of the Sandwich Islands : 
— Honolulu : Chief, Capt. G. L. Tupman, 
astronomer; Observers, J. W. Nichol, 
astronomer and photographer; Lieut. F» 
E. Ramsden, R.N., astronomer and photo- 
grapher. Hawaii : Chief, Prof. G. Forbes, 
astronomer; Observer, H. G. Barnacle, 
astronomer. Kauai : Chief, R. Johnson, 
astronomer; Observer, Lieut. E. J. W. 
Noble, R.E.M., astronomer. 

" 5. District C. Rodriguez : Chief, 
Lieut. C. B. Neate, R.N., astronomer; 
Observers, C. E. Burton, astronomer and 


photographer; Lieut. R. Hoggan, R.N., 
astronomer and photographer. 

'' 6. District D. Christchurch (New 
Zealand): Chief, Major H. Palmer, R.E.; 
Observers, Lieut. L. Darwin, R.E., 
astronomer and photographer ; Lieut. H* 
Crawford, R.N., astronomer. 

** 7. District E. Kerguelen Island : 
General Chief, Rev. S. J. Perry; Deputy, 
if necessary, Lieut. C. Corbet, R.N. 

" Sub-divisions of the Kerguelen Is- 
land : — Christmas Harbour : Chief, Rev. 
S. J. Perry, astronomer and photographer ; 
Observers, Eevs. W. Sidgreaves, astrono- 
mer ; Lieut. S. Goodridge, R.N., astrono- 
mer ; J. B. Smith, astronomer and photo- 



grapher. Port Paliser : Chief, Lieut. C. 
Corbet, R.N. ; Observer, Lieut. G. E. 
Coke, R.N. 

" 8. In addition to these gentle- 
men, three non-commissioned officers or 
privates of the Corps of Royal Engineers 
will be attached to each of the five dis- 
tricts, and will be under the direction of 
the chief of each district.'* 

Expeditions for observing the transit 
have also been sent to various parts of 
the world by the Governments of France, 
Germany, Italy, Holland, Russia, and the 
United States of America. 


CondvAing Remarks. 

It has been stated that the solar paral- 
lax, as generally adopted by astronomers 
in the present day, would place the Sun 
at a distance of ninety-one and a half 
millions of miles from the Earth. This 
element puts us at once in possession of 
the distances of all the planets from the 
Sun. In this manner we arrive at a 
knowledge of the dimensions of the 
system of which the Earth forms one of the 
constituent bodies. We find the extreme 
planet of the system revolving round 
the Sun to be situated at a distance 
of nearly three thousand millions of 


miles. We discover that the planets 
are bodies of immense size, several of 
them vastly exceeding the Earth in mag- 
nitude. We obtain from the same source 
a knowledge of the magnitude of the 
orbits of the satellites which are found to 
accompany the larger planets of the sys- 
tem. Once in possession of a knowledge 
of the solar parallax, we are enabled to 
determine the masses of the planets by 
comparing them with the suns mass. 
The same important element gives us 
information respecting the amazing velocity 
with which the planets travel in their 
orbits, and the consequent enormous in- 
tensity of the sun's attraction, which pre- 


vents them from flying off into space. If 
we direct our attention to the system 
of comets, we are equally struck with 
the light thrown upon the movements of 
those mysterious bodies by our know- 
ledge of the solar parallax. We obtain 
an instructive insight into the amazing 
.velocity with which in many instances 
they travel in their orbits, we measure 
the dimensions of their orbits, and com- 
pute with precision the distances to which, 
when travelling to their aphelia, they 
recede into the illimitable depths of space* 
The planet Neptune revoWes round the 
sun at a distance of nearly three thousand 
millions of miles from the Earth. The 


great comet of 1858, when passing 
through the aphelion of its orbit, recedes 
to a distance of thirty thousand millions 
of miles from the Earth, and yet this 
enormous distance amounts to only a 
seven hundredth part of the distance of 
the nearest of the fixed stars. It is to be 
remembered furthermore, that whatever 
knowledge we possess respecting the dis- 
tances, magnitudes, and masses of the fixed 
stars, is dependent on the same element. 
As soon as we have determined the radius 
of the Earth's annual orbit round the Sun, 
we can make use of the diameter as a new 
base-line, and upon this immensely im- 
proved vantage ground proceed to deter- 



mine the distances of the stars. When 
Copernicus propounded the true system of 
the universe, it was argued by his oppon- 
ents that according to his views the 
stars ought to present an annual varia- 
tion of aspect and position depending upon 
the motion of the Earth in its orbit. 
Copernicus met this objection by remark- 
ing that the whole solar system was a 
mere point in comparison with the sphere 
of the fixed stars. It is worthy of note, 
that until a comparatively recent period, 
this was the only reply which could be 
given to the opponents of the Copemican 
theory. In the present day several stars 
have been detected, presenting parallaxes 



of such undoubted magnitude, that we are 
enabled with perfect confidence, to assign 
their distances from the Earth. The re- 
sults which have been arrived at by re- 
searches in this branch of astronomy, 
are calculated to inspire with awe all 
who devote their attention to the subject. 
Even the masses of the stars have been, 
in some instances, determined; and we 
arrive in this manner at the startling 
conclusion that the luminaries of the 
stellar vault are bodies of immense size, 
rivalling the Sun in magnitude and splen- 
dour. It has been an opinion generally 
held by astronomers, thsit the stars 
are distant Suns. Our knowledge of 


the value of the solar parallax, com- 
bined with the results of recent researches 
in stellar astronomy, assure us beyond all 
doubt of the reality of this fact. 

We shall conclude with a statement 
of the steps by which the human mind 
is enabled to ascend in succession to the 
contemplation of these lofty truths. 
First, the astronomer measures a base 
line seven or eight miles in length upon 
the Earth's surface. Combining this 
result with the solar parallax, he deter- 
mines the distances of the planets from 
the sun, their magnitudes and masses, and 
the velocities of their orbital movements. 
He computes the dimensions of the orbits 


of comets and meteor streams, and assigns 
with precision the distances to which they 
recede into space when they have reached 
the aphelia of their orbits. Finally, 
assuming as a new base line for his re- 
searches the diameter of the Earth's orbit, 
a line measuring a little more than a 
hundred and eighty millions of miles in 
length, he determines the distances and 
masses of the stars. He computes 
the velocities with which they travel 
in space, and compares them in this 
respect with the movement of the solar 
system in space. Nay, the spectroscope 
informs him respecting the materials 
of which those remote bodies consist, and 


thus teaches him another important fact 
in support of the grand doctrine that the 
Sun is no other than a star, and that the 
innumerable bodies of the stellar vault 
are magnificent globes of light, rivalling 
the Sun in magnitude and splendour. 
We have here presented to us a striking 
instance of the sublimity of the views 
respecting the immensity of the physical 
universe which the science of astronomy 
has disclosed to the researches of the 
human mind. 




» . *• 



• V