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THE

€xmsxt 0f ^tms uxm tlje Sun:

A TRANSLATION OF THE CELEBRATED DISCOURSE THEREUPON,

REV. JEREMIAH HORROX.

CUBATE OF HOOLE, (1639,) NEAR PRESTON;

TO WHICH IS PRKFIXEI

A m:b]veoiii

XjIIPE J^ISTJD XJ^^BOTJI^S.

REV. ARUNDELL BLOUNT WHATTON, B.A.,LL.B.

LONDON:
WILLIAM MACINTOSH,

24, Paternoster Row.

^z??^

11^

In i^emoriam

PATRIS DILECTISSIMI

GUL : ROB : WHATTON, F.R.S. : F.S.A., ETC.,

VIRI LITERIS HUMANIORIBUS EXIMTE ERUDITI,

li HAS EGREGII ADOLESCENTIS RELTQUIAS,

QUEM VIVUS IPSE EST MIRATUS,

CUM QUO MORTUUS, FAS EST CREDERE, CONSORS,

COLLIGENDAS ET IN LUMEN PROFERENDAS CURAVIT

FILIUS AMANTISSIMUS

A. B. W.

CONTENTS.

PAGE

Dedication -_-__--- Hi

Preface ________ vi

Memoir --------- l

Treatise —

Chapter I. — The occasion, excellence, and utility of

the Observation _ _ _ - 109

„ II. — Account of the Observation - - 117

„ III. — What others observed, or might have

observed, of this Conjunction - 127

„ IV. — It is proved that the spot observed in

the Sun's disc was really Venus - 136

„ V. — The Examination of the apparent Lon-
gitude and Latitude of Venus from
the Sun 145

„ VI. — The alteration of the apparent into the

true situation of Venus - - 150

„ VII. — An Inquiry into the Time and Place
of the true Conjunction of Venus and
the Sun _ - . _ . 153

„ VIII. — The Demonstration of the Node of

Venus ------ 156

„ IX. — The beginning, middle, and end of the

Transit are shewn - - - - 158
A 2

VI CONTENTS.

PAGE

Chapter X. — An Examination of the Calculations of

Astronomers respecting the foregoing 161

„ XL — The Calculation of Copernicus - - 164

„ XII. — The Calculation of Lansberg - - 170

„ XIII. — The Calculation of Longomontanus - 174

„ XIV.— The Calculation of Kepler - - 176

„ XV. — Correction of the Motions according to

Rudolphi ----- 181

„ XVI.— On the Diameter of Venus - - 187

„ XVII. — On the Diameters of the rest of the
Planets, of the Proportion of the
Celestial Spheres, and of the Parallax
of the Sun 202

PREFACE

When my father was engaged in writing the
Biographical department of the history of Lan-
cashire, he was naturally led to consider the
merits of Jeremiah Horrox, the youthful
astronomer of that county ; and he was so much
impressed with his distinguished scientific attain-
ments that, finding it impossible from want of
space to do him justice in those pages, he proposed
on some future occasion to publish his life in a
separate form. Accordingly, he ascertained the
precise value of his discoveries, and gathered
together much interesting detail connected with
his personal history; and he also set about pre-
paring a translation of his celebrated Treatise upon
the transit of Venus over the Sun. But he did

Vlll PREFACE.

not live to complete this work. It would appear
that much material had been accumulated, but
that the arrangement of it had not even been
commenced. To him however belongs the credit
of being the first and only person who has
undertaken to supply what is acknowledged to be
a deficiency in the literature of our country ; and
there can be no doubt that, if his life had been
spared a little longer, he would have produced a
most interesting and instructive volume. Professor
Rigaud, of Oxford, wlio was his fi?iend and associate
in these pursuits, says in his " Correspondence of
Scientific Men of the 17th century," that "the
late W. R. Whatton, Esquire, had made con-
siderable collections for a life of Horrox, which he
intended to have prefixed to a new edition of the
Venus in sole visa, when death in 1835 deprived
the world of the fruit of his inquiries."

Since then no further attempt of this kind has
been made to recognize the merits, or to perpetuate

PREFACE. IX

the memory of Horrox. Of late years, however,
his name, associated with the names of other
persons of distinction, has been brought before
the public from time to time by various speakers
at literary and scientific meetings, especially in
Lancashire. Thus, in an address delivered in
Liverpool on the celebration of the centenary of
the birthday of Roscoe, the Rev. Dr. Hume says :
" neither is Roscoe the first man of high intellectual
attainments that Liverpool has numbered among
her sons. More than two centuries have elapsed
since Jeremiah Horrox, a native of Toxteth Park,
and then only twenty years of age, observed the
first transit of Venus across the Sun. His high
attainments at that early period, in astronomy
and pure mathematics, have been the admiration
of succeeding men of science. His reputation
may be said to have reached his native country
from the continent, by the publication of his
treatise Venus in sole visa, at Dantzic ; and it is

X PREFACE.

only of late years that Professor Rigaud and
Mr. Whatton have laboured successfully to do
justice to his memory."

The fame of Horrox has also been disseminated
through the instrumentality of the press, letters
having occasionally appeared, complaining that no
record of his discoveries has been published in
our native tongue, and commending the subject
to the attention of those competent to deal with
it. One of these, taken from the columns of a
newspaper, was, a few months ago, enclosed to me
by a friend, in which the writer thus alludes to
the remarks of Professor Rigaud already quoted :
" A life of Horrox is much wanted. Very little
is known indeed of his daily work, but that little
is such as to create a desire of knowing as much
about him as possible. The particulars gathered
up by Mr. Whatton will, I trust, be heard of, and
make us better acquainted with one whom Sir J.
Herschel justly calls ^the pride and boast of

PREFACE. XI

British astronomy.' And surely the Venus in
sole visa ought to have an English edition, for if,
as Grant remarks, 4t does not redound to the
credit of England that this exquisite relic of one
of her most gifted sons should have been allowed
to see the light in a foreign land/ neither does it
evince a due regard for the labors of scientific
men that this famous dissertation has yet to be
published in our own country. I should be very
much obliged for any information of the Whatton
papers." Upon receipt of this extract, I searched
for anything in my possession that might be
available, and found sundry memoranda, and
some interesting letters from Mr. Rigaud, the
perusal of which led me to prosecute the inquiry
until I was enabled to carry out, in some degree,
the original design, by preparing a Memoir of the
life of Horrox, and a translation of his discourse
upon the transit of Venus.

It is felt that this little work is a very imperfect

Xll PREFACE.

substitute for what mi^ht have been achieved by
abler hands ; but being in possession of the details
of Horrox's personal history, I should scarcely
have been justified in withholding them, as it is
a hopeless task for a stranger, on the spur of the
moment, to attempt to look for such particulars
as may be collected from a lengthened course of
general reading. My aim has been to shew the
value of his labors, and to ^x the place they
occupy in the history of science ; and also to
make his merits more widely known than they
are at present, in order that he may enjoy in the
estimation of the public, the rank which he already
holds in the opinion of the learned. Accordingly,
such letters and quotations as were written in
Latin are here given in English. This will not
occasion any confusion, as those which are trans-
lations may be distinguished at a glance from
others which have been merely copied.

It will be observed that the name of Horrox is

PREFACE. Xlll

sometimes spelt Horrocks, I have carefully ex-
amined which orthography is the more correct,
and have adopted the former, as the name is so
entered upon the College Register, and was
always so written by Crabtree and Wallis.
Grant and some recent authors use the latter
method. The difference is of no importance, and
it is only noticed here by way of explanation.

In the translation of the Venus, I have endea-
voured to adhere closely to the original, and have
taken the text of Hevelius as a basis, merely
correcting the punctuation from the Greenwich
manuscript where it was necessary to do so, and
altering the arrangement of the sentences where
the difference of language required it. The
Dantzic edition is accompanied by voluminous
notes which are appended to the end of each
chapter, and at first I thought of giving them
precisely in the order in which they stand.
Afterwards it occurred to me that it would be

XIV PREFACE.

better to print Horrox's dissertation entire, and
to collect tlie notes together, and put them at the
end by themselves, so as to present a clearer view
of the treatise, without having the attention con-
tinually called off, sometimes indeed when there
is no difficulty that needs to be explained At
length, however, I decided to omit them altogether,
as they contain nothing of importance connected
with Horrox's personal history, and are full of
error upon those points which they were designed
to elucidate. The mistake that Hevelius has
made in his statement of the parallactic angle is
an instance of this, and has given rise to many
faulty corrections in his comment. Flamsteed
noticed it, and did not consider his remarks a
very valuable appendage ; for in a letter to
Collins, he says: "Having well perused the
Venus in sole visa^ I know not what can be
added; the notes of Hevelius I find generally
useless, and those on the 6th chapter absolutely

PREFACE. XV

false." The side-notes which are found in the
printed edition have also been excluded, as it is
certain that they are not authentic. These
accretions being removed, the tract appears in the
same form, though not in the same dress, as that
which it had when it came from the pen of its
author ; and the reader is enabled to peruse it
without distraction, and to arrive at an indepen-
dent opinion of its merits.

In writing what follows, I have consulted
Fqjrguson, Delambre, Montucla, Grant's Treatise
upon Physical Astronomy, and the suggestions of
Professor Rigaud contained in the manuscripts
in my possession. The correspondence between
Huygens and Hevelius is taken from Huygens'
papers preserved in the public library at Ley den.
No doubt there is abundant room for criticism ;
but it may be pleaded that the task was wholly
unsought, having devolved on me from circum-
stances over which I had no control, but from

XVI PREFACE.

the obligation of which it would have been
imworthy to retreat. Should these pages be
deemed insufficient for the purpose which has
been announced, I can only say that I shall be
much gratified if some one, more competent than
myself to do justice to the memory of Horrox,
will make use of the material, here gathered
together, to produce a better work. And I may
add, as a further extenuation, that they have been
penned in such brief intervals of leisure, during
the last few months, as remained over and above
the discharge of more important duties ; so that
I may fairly take refuge in Horrox's own words,
" Ad majora avocatus, quae ob hsec parerga
negligi non decuit."

39, Weymouth Street, Portland Place,
July 2Qth, 1859.

MEMOIE or JEEEMIAH HOEEOX.

We are familiar with the names of some writers
who have contributed scarcely anything of real
value to the literature of their country ; whilst
we are ignorant of the worth of many others
who occupy a distinguished position in the com-
monwealth of science. Thus few persons have
heard of Jeremiah Horrox, although his merits
as an astronomer have been acknowleds^ed
by the most eminent scientific men who have
succeeded him. But he lived in obscurity, and
died young. He was not permitted by an all-
wise Providence to carry on his investigations for
more than a few short years. He did not even
enjoy the satisfaction of publishing his own
discoveries. He was cut off in the midst of use-
fulness, and others have entered into his labors.
Hence he is comparatively unknown. Happily
his performances, as a skilful pioneer for the
advancement of knowledge, are well authenticated,

and are of sufficient importance to make his name
illustrious. He paved the way for some of the
most brilliant triumphs of the human intellect.
Learned men have freely acknowledged this ; and,
in tender regard for the memory of one who
expired whilst full of hope and promise, have
constituted themselves the trustees of his reputa-
tion, and set their seal to his ability and worth.
It is thought, therefore, that the details of his
history may not be unacceptable, especially as his
valuable services are now about to be recognised
by a monument raised by subscription ; and that
the disinterested efforts of this young philosopher
in search of truth cannot fail to enlist the
sympathy and admiration of all who are made
acquainted with them.

He was born at Toxteth Park, near Liverpool,
in the year 1619. Little is known as to the
position and circumstances of his family ; but in
the scanty notices of him that remain, he is
generally spoken of as a person of humble origin.
It seems probable, however, from his having been
classically educated, and destined for one of the
learned professions, that this representation is

3

rather overdrawn, and that the Horrox family
were not so obscure as they have been described.
Liverpool was not then a seat of industry, enter-
prise, and intelligence, but a place of comparative
insignificance; and Toxteth, far from being a
wealthy and elegant suburb, was only a little
village about three miles distant from it in the
County Palatine of Lancaster. It is therefore
extremely unlikely that he could have received
any considerable advantages in his native place ;
and in those days, on account of the expenses of
travelhng and residence, it was not usual for
a young man entirely without means to be
sent to the ancient seats of learning. Hence we
are led to conclude, either that his parents were
in easy circumstances, and able to value the
benefits of a liberal education, or that the genius
of young Horrox attracted the attention, and
secured the patronage of some person of distinc-
tion. Upon this and other points connected with
his opening history, it is to be regretted that we
possess so little information ; for the auspices
under which life commences, and the incidents of
childhood, not unfrequently form an interesting

B 2

page in the biography of great men. The school
campaign, with its successes and failures, its
schemes, friendships and amusements affords ample
scope for the display of a boy's taste, talent, and
disposition, and gives some indication of what may
be expected from him in after life. Thus Isaac
Newton, withdrawing from the noisy playground,
spent his leisure hours in the construction of
w^ater-clocks, and other mechanical contrivances ;
Halley set up a sun-dial, and had observed the
variation of the needle before he left school;
Watt took an early pleasure in the manual exercises
of his trade ; James Ferguson made a watch of
wood-work when quite a boy; and it is reason-
able to suppose that Horrox in like manner shewed
a partiality for the pursuits in which he afterwards
distinguished himself In those days lads of more
than ordinary promise were admitted to the
University much younger than they are at present,
especially if introduced by an influential patron ;
hence we are not surprised to find that as soon as
Horrox had received the rudiments of education
at Toxteth, he was entered at Emmanuel College,
Cambridge, before he had attained his fourteenth

year. The following is a copy of the Register:

" Jeremiah Horrox. Born at Toxteth, Lancashire.
Entered Sizar, 18 May, 1632."
His having been placed on the college foundation,
tends to confirm the surmise that his parents were
not affluent, and that his advantages had hitherto
been limited. But we know from the history of
others who have attained to eminence in the
several departments of learning, that the aspira-
tions of genius cannot be w^holly crushed by
poverty, but that it will rise superior to circum-
stances, as surely as a blade of grass breaks through
a clod of earth, and points its spire to the heavens.
Horrox hailed with delight his removal from the
village school to a seminary abounding with the
means of intellectual improvement, and resolved
to make the most of his opportunities. Having
read the few subjects which were then included
in an academical education, he explored the wide
field of classical literature, readily yielding to its
allurements, and regarding them as more than a
compensation for any amount of labor. He
particularly cultivated the best Latin authors, in
order to become familiar with a language which

was then the only medium of communication
amongst the learned. In this way he acquired a
large store of general knowledge, and was enabled
to gratify his taste for any favourite pursuit. In
a word, he drank deeply at the Castalian fount,
and by his industry repaid the effort that had been
made to send, him to Cambridge.

But whilst he was fully capable of appreciating
the advantages of an University, he did not remain
at college longer than was absolutely necessary,
being desirous of preparing for the work of the
ministry, which he had adopted as the profession
of his choice. Some doubt has been entertained
as to whether he was ever admitted into Holy
Orders. Young men are now required to be
twenty-three years of age before they can be
ordained, whereas he was not more than twenty.
This objection might easily be answered by the
fact that two centuries ago the question of age
was not so strictly attended to, the Bishop exer-
cising a discretionary power. But fortunately we
are able to place the matter beyond conjecture ;
for in a treatise by John Gadbury, the compiler
of almanacks, there is mention of

" Ephemerides of the planetary motions, eclipses, con-
junctions, and aspects for fifty years to come, calculated
from the British tables, composed first by the Reverend
Mr. Horrox, and first published by Jeremy Shakerley."

He commenced his ministerial labours in his
native county, being ordained to the curacy of
Hoole, in Lancashire. This place formerly con-
sisted of a narrow strip of land, having a large
extent of moss on the east and west, the waters of
Martin-Mere and the Douglas on the south, and
the overflow of the Ribble on the north. It was
therefore almost an island ; and though doubtless
an open situation for an astronomer, it could not
have been a very agreeable residence. This
once desolate spot is now a thriving township
containing about a thousand inhabitants. The
hand-loom and power-loom furnish, their chief
employment, though much of the land has been
reclaimed, and is under tillage. The Parish.
Church, which was erected in the fifteenth cen-
tury, is dedicated to Saint Michael, and consists of
a plain brick nave without side- aisles, a chancel,
and a stone tower supported by four pillars.
There has long been an endowment for educa-

tional purposes, and about eight years ago a good
national school and school-house were built after
a plan by the government architect, at a cost of
£600. Mr. Horrox's first letter from Hoole is
dated June 1639, and he continued to reside
there for some little time. There is no local re-
cord of his official connexion with the place, as it
was not then constituted an ecclesiastical district,
being merely a chapel of ease to the mother
church of Croston, the register of which is com-
paratively modern ; but that he was curate of the
parish is a matter of history, for to omit the
testimony of other writers, we may mention that
Costard, an eminent astronomer who lived at the
beginning of the last century, designates him as
'" a young clergyman of Hoole, near Preston."
There is reason to believe that, besides his minis-
terial avocations, he was in some way engaged in
tuition, as he speaks of his " daily harassing
duties " during the time he resided there.

It was whilst he was at the University that he
first turned his attention to the study of astro-
nomy. With a love of the sublime, and naturally
fond of speculation, in the contemplation of the

works of God he found a pursuit at once congenial
to his taste, and calculated to bring into active
exercise the highest powers of his mind. It did
not satisfy him to look with an untutored eye
upon the sun, the moon, and the stars shining in
the firmament of heaven ; he desired to learn
something of their magnitudes, their distances,
the periods in which they perform their revolu-
tions, and the laws by which they are governed.
" It seemed to me," he says, " that nothing could
be more noble than to contemplate the manifold
wisdom of my Creator, as displayed amidst such
glorious works ; nothing more delightful than to
view them no longer with the gaze of vulgar
admiration, but with a desire to know their
causes, and to feed upon their beauty by a more
careful examination of their mechanism." Ani-
mated with these convictions, he prepared to
enter upon the study of astronomy by first
cultivating with the utmost patience the aptitude
for mathematics which he had evinced from his
youth. But he had to work without assistance ;
for at that time, no branch either of mathematical
or physical science was taught at Cambridge. In

10

this respect she was considerably behind her sister
University. Many scientific men had already
emanated from the cloisters of Oxford. Bacon,
Sacrobosco, and Greathead, were educated there.
In short, the renown which Cambridge has ac-
quired, and now enjoys in this kind of learning,
is of a comparatively recent date. Certainly she
had no school for science before the commence-
ment of the seventeenth century. This was owing
to the endowments of Oxford being older and
richer, and to its collegiate system being earlier
established. Thus he had no professional instruc-
tion; he could not obtain in the University the
books he required ; nor was there any one capable
of advising him as to which it was most desirable
for him to procure. This was particularly the
case in reference to astronomy, which had scarcely
yet taken root in our land. Its votaries had no mea-
sure of experience to consult, no body of doctrine
to quote. Not a single public observatory had
been erected either in England or France, nor
indeed had astronomical observation as yet be-
come fairly organized. The difficulty there was
in obtaining works on physical science, may be

11

illustrated by the following circumstance. Some
time ago Mr. de Morgan met with a book which
had formerly belonged to Horrox, and upon ex-
amining it, he found that it contained a written
catalogue of the library which, at some period of
his life, he seems to have possessed : —

Lansbergii Progymn. de
motu soKs.

Longomontani Astron. Da-
nica.

Magini Secunda MobHia.

Mercatoris Chronologia.

Plinii Hist. Natiiralis.

Ptolemaei Magntim Opus.

Regiomontani Epitome.

Torquetmn.

Observata.

Albategnius.

Alfraganus.

J. CapitoKnus.

Clavii Apolog. Cal. Rom.

Clavii Comm. in Sacrobos-

cum.
Copernici Eevolunitiones.
Cleomedes.
Julius Firmicus.
Gassendi Exerc. Epist in

Phil. Fluddanam.
Gemmae Frisii Radius As-

tronomicus.
ComeHi Gemmae Cosmo-

critice.
Herodoti Hjstoria.
J. Kepleri Astron. Optica.

Epit. Astron. Copern.

Com. de motu Martis.

Tabulae Rudolpbinae.

Rheinoldi Tab. Prutenicas.
Com. in Theor. Pur-

bacbii.
Theonis Comm. in Ptolom.
Tyc. Brabaei Progymnas-

mata.

Epist. Astron.

Waltheri Observata.

12

Now it is very remarkable that, so far as we can
ascertain, not one of these books had been pub-
lished in our own country. The above interesting
relic was sent to the authorities of Trinity College,
Cambridge, with a request that it might be care-
fully preserved. The student of to-day can hardly
enter into the feelings of a young man thirsting
for knowledge, and circumstanced in the manner
just described. Not to mention the public lec-
tures, libraries, associations, and other advantages
which belong to an University, every department
of knowledge is represented to the general reader
by so great an abundance of literature, that the
only difficulty is to make the best selection. Ele-
mentary treatises are now published at prices
which place them within the reach of the poorest
scholar. And after all, books are the best teachers.
The minds of many who have immortalized them-
selves and reflected honour upon their country,
have been formed without any other assistance.
But in the seventeenth century books were scarce
and dear. We conclude therefore that there are
no such drawbacks to be experienced now, as
those which oppressed the student in science

13

before the days of popular literature. Horrox
labored under the greatest disadvantages, and
hence he has all the more merit. He toiled up
the sides of Parnassus without friendly assistance
or encouragement. He meditated alone upon
the abstruse subjects of philosophical enquiry.
Having procured such treatises as he could afford
to purchase, he qualified himself for the successful
pursuit of the sublime science with which his
name will ever be associated. But he has recorded
his troubles in touching language : —

" There were many hindrances. The abstruse nature
of the study, my inexperience, and want of means dis-
spirited me. I was much pained not to have any one to
whom I could look for guidance, or indeed for the sym-
pathy of companionship in my endeavours, and I was
assailed by the langour and weariness which are insepar-
able from every great undertaking. What then was to
be done ? I could not make the pursuit an easy one,
much less increase my fortune, and least of all, imbue
others with^ love for astronomy ; and yet to complain of
philosophy on account of its difficulties would be fooHsh
and unworthy. I determined therefore that the tedious-
ness of study should be overcome by industry ; my poverty
(failing a better method) by patience ; and that instead of a

14

master I would use astronomical books. Armed with
these weapons I would contend successfully ; and having
heard of others acquiring knowledge without greater help,
I would blush that any one should be able to do more
than I, always remembering that word of Virgil's
'^ 'Totidem nobis animaDque manusque.' "

Although astronomy had not taken firm root
in our land before the time of Horrox, elsewhere
it had considerably revived. Its cultivation in
Europe was the commencement of a new aera.
For the first two hundred years after its introduc-
tion upon the continent, little ground was gained ;
but subsequently men of genius and strength
arose, who efifectually exposed the absurd hypothe-
ses then in vogue, put the science upon a right
basis, and by delivering it from the trammels of
superstition, led the way in a career of perpetual
improvement. Thus Copernicus had re-established
the old Pythagorean doctrine which places the
sun in the centre of the system. This at once
simplified all the planetary movemeifts. The
apparent revolution of the heavens was explained
by the diurnal rotation of the earth. Tycho
Brahe had enriched the science by a series of
accurate observations. He had detected the lunar

15

inequality, known as the variation ; he had proved
the path of the comet of 1577 to run out beyond
the moon's orbit ; and he had prepared, as the most
valuable product of his labors, a catalogue of 777
of the fixed stars. Kepler had explained the
laws of celestial motion. He had discovered that
the planets move in elliptical orbits, with the sun
in the lower focus ; that the radius-vector describes
equal areas in equal times ; and that the squares
of the periodic times of any two planets are to
each other as the cubes of their mean distances
from the sun. He had also some knowledge of
the laws of gravitation. Galileo had greatly ex-
tended the limits of astronomical vision. Havino:
heard that, by a combination of lenses, objects
might be made to appear nearer to the eye, he
ascertained the truth of the report ; and improved
the invention so much, that he was soon able to ex-
plore the heavens with his telescope, and to reveal
new wonders to mankind. Milton alludes to his
discovery of the inequalities of the moon's surface :
" The moon whose orb,

Through optic-glass, the Tuscan artist views

At evening, from the top of Fesole

Or in Yaldarno, to descry new lands,

Eivers, or mountains on her spotty globe/'

16

Besides this he had detected the phases of the
planet Venus, the four satellites of Jupiter, the
spots on the Sun, Saturn's ring, and a multitude
of stars too small to be seen with the naked eye.
Thus by the genius of a few great men, the science
was completely reconstructed, and enriched with
much valuable learning. Its advancement was
also hastened by the preparation of tables for
facilitating the long and tedious calculations
inseparable from astronomical pursuits. But im-
provement is unsteady in every department of
human industry. Like the motion of the heavenly
bodies, it is at one time accelerated, and at another
retarded. An apostle or reformer suddenly ap-
pears, and promotes the welfare of his fellow men
by rectifying abuses, and by bringing to light
important truths. After he has delivered his
message a calm ensues which lasts until another
master-spirit arises. It is so in trade, politics,
literature, and science ; and it is wisely ordered
that time should be allowed for testing by experi-
ment the principles that have been broached.
The three astronomers last named were contempo-
raries ; and their departure was followed by a

17

period of comparative inactivity. This was bow-
ever very soon relieved by the appearance of
Horrox, upon wbom tbeir mantle may be said to
have fallen. But he did not take up the pro-
phetic strain from the point where tbey had left
it ; he did not see the writings of bis famous
predecessors until after he had labored at
astronomy for some time; be bad to work out
the grammar of the science for himself; to toil
over ground tbat bad already been surveyed ; and
being witbout friendly assistance, bis worst fears
of going astray for want of an able adviser were
unfortunately realized. Happening to meet with
a treatise by D. H. Gellibrand, a professor of
astronomy, in London, in which the works of
Lansberg were spoken of witb unqualified praise,
it occurred to him tbat it might be advantageous
to possess them ; and after some difficulty, he
succeeded in obtaining the Uranometriam^ the
Tabulas Perpetuas^ and the Progymnasmata de
motu Solis. Pleased witb the acquisition, be was
induced to neglect the more valuable works of
Tycho and Kepler, and to employ bimself in
computing Ephemerides from the tables of the

c

18

Flemish mathematician, not suspecting the spe-
ciousness of the titles which he prefixes to his
calculations ; but after a considerable time spent
in this manner, he began to make his own
observations, using these Ephemerides to point
out the situations of the planets, and hence
determining when their conjunctions, their ap-
pulses to the fixed stars, and other remarkable
phenomena were to be expected.

In the year 1636, he made the acquaintance of

William Crabtree, a draper, residing at Broughton,

near Manchester, who had long been devoted to

the study of astronomy; and a correspondence

was at once commenced between them upon the

various subjects connected with their favourite

pursuit. This intercourse was the signal for

increased assiduity on the part of both, and proved

in one respect particularly useful to Horrox — it

opened his eyes to the imperfection of Lansberg's

tables. Hitherto, upon noticing a disagreement

between them and his own observations, he had

supposed the error was attributable to himself;

and although the same result invariably followed

after repeated trial, and there appeared to be no

19

way of removing the discrepancy, rather than
doubt the accuracy of one for whom he entertained
so high an opinion, he continued equally self-
suspicious, and was almost tempted to despair of
success. But upon comparing notes with Crabtree,
and perceiving that their observations entirely
coincided, he called the attention of that gentleman
to the circumstance, and was by him advised for
the future to put less faith in the dictates of
Lansberg. This led to a more rigorous examina-
tion, both of the tables, and also of the principles
upon which they were based ; and it soon became
evident that much of what was put forth as truth
was incapable of demonstration.

Emancipated from this tyranny of error, Horrox
gathered fresh courage to proceed ; he strove to
redeem the time he had lost by redoubling his
exertions ; and afraid of being again misled by the
misrepresentations of others, he learned to place
more dependence upon his own judgment. At
the same time he determined to avail himself of
whatever aids and appliances he could obtain :
new books and instruments were procured ; and
instead of seeking seclusion as before, he verified

c2

20

his operations by a regular correspondence with
Crabtree. Besides this agreeable intercourse, the
two friends presently became known to Dr. Samuel
Foster, the Praelector of Gresham College, an able
ally, whom they occasionally consulted.

The removal of a false impression, such as the
one now described, if it does not give an actual
impulse to the mind, at all events restores its
wasted powers, and turns them to the best
account. The clouds being dissipated, a new
light breaks in, by which we can review the
experience of the past, ascertain the strength of
our present position, and lay down fresh plans
for the future. Having escaped from the empiri-
cism by which his expanding genius had so long
been circumscribed, Horrox sought out the
writings of Kepler, which Lansberg had stigma-
tized as " falsa et erronea, imo absurda, et inter
se pugnantia." He instantly perceived their value.
He found that instead of being composed of
fanciful speculation, or arbitrary assertion, as he
had been led to believe, they contained discoveries
of such importance as to constitute a new era in
the history of astronomy ; and he received with

21

transport the elucidation of general laws which
were evidently the conclusions of a patient and
legitimate induction. He also fully appreciated
the merits of the Rudolphine tables, and con-
sidered them incomparably superior to those of
Lansberg, as the hypotheses were well established,
and reconcilable with one another. To amend
these tables was now his chief desire. It occurred
to him that they might be improved by changing
some of the numbers, but retaining the hypotheses;
and that he would be abundantly repaid for this
arduous undertaking by the opportunity it would
afford for deducing general principles, and es-
pecially for verifying Kepler's laws. Accordingly
he applied himself to this task with unwearied
diligence ; and by making frequent observations,
and altering the numbers to suit them where it
was necessary, he brought the tables to a surprising
degree of accuracy, and in doing so, materially
added to his information. Speaking of the gratifi-
cation he derived from the writings of Tycho and
Kepler, and the incentive they were to renewed
application, he says : "It was a pleasure to me
to meditate upon the fame of these great masters

22

of science, and to emulate them in my aspirations";
and accordingly we find that whilst he fully
recognized the merits of the illustrious Dane as
a skilful observer, his sagacious intellect clearly
apprehended the truth of Kepler's doctrines, the
universal acceptation of which he sought to pro-
mote.

The first efforts of Horrox's pen were directed
towards the preparation of a treatise, the object
of which was to refute Lansberg's theories, and
to establish a more correct system of planetary
distribution. He thought it important to the
interests of science that the false hypotheses which
then prevailed should be thoroughly exposed, and
a misapplication of time and talent prevented for
the future ; and he wrote several learned disserta-
tions, some of which were re-cast from beginning
to end as often as it appeared to their author
that they might be improved by a different mode
of treatment. To specify a few of these, we may
mention that at the close of the year 1637 he
commenced a treatise entitled ^'Jeremice Horroccii
Anti-Lanshergianus^ sive disputationes in astrono-
miam F. Lansbergii, quihus perspicue demonstra-

23

tur^ hypotheses suas nee ccelo nee sibi conseniirey
Having completed upwards of four disputations,
he changed his plan, and re-modelling the whole,
entitled it ''^ Astronomice Lanshergiance censura
et cum Kepleriana corrvparatioy Of this he wrote
three copies agreeing with each other as to
their object and arguments, but differing in the
mode of discussion, and in their respective lengths:
of the first copy he only finished one chapter, of
the second nearly four, and of the third upwards
of five. This favourite tract appears again in
another dress, being designated as ^'' Explicatio
hrevis et perspicua diagrammatis Hipparchi^ et
Lanshergii erroris^^ but it is in substance the
same as the former ones.

He next wrote a treatise against Hortensius, a
follower of Lansberg, who had attempted un-
warrantably to depreciate the merits of Tycho ;
and here also he seems not to have grudged the
labor of repeated efibrts in order to produce an
essay that should be perfectly conclusive. Thus
we have firstly a paper inscribed " Contra
Hortensii prcEfationem^ Lanshergii Commenta-
tionihus de motu Terrce prcejixamy This was

24

afterwards re-written and styled " Anti-Lansher-
gianus, sen astronomice verce vindicice. Pars
prima in qua respondetur Martinii Hortensii
cavillis adversus Tychonemy Its title was again
changed to '^ Dissertatio cum Martino Hortensio
de asironomia Tydionicay It was next called
" Astronomice Tychonicoe apologia^ adversus Hor-
tensii cavillasy And lastly, ' ' Epilogus ad Martinum
Hortensiumy in quo cavillis adversus Tychonem
respondetur.""

There are also other tracts upon similar subjects ;
for example, the commencement of a work entitled
^^ Prceludium Asironomicum,'' of which the first
book only ''& motu solis'' was in hand, a chapter
of it upon the sun's horizontal parallax being
entirely finished ; the beginning of another treatise
inscribed " Anti-Lanshergius sive asironomia vin-
dicata " ; and part of another, in which it was
proposed to institute a comparison between various
hypotheses of the system of the universe, which
is inscribed as ^^ Paris Astronomicus^ seu Judicium
de vera asironomia^ quo trium astronomorum
Keplerij Longomontani^ Lanshergii tabulce astro-
no7nicce, et hypotheses ^ seu tahularum fundamental

25

rationihus physicis, demonstrationihus geometricis,
et ohservationihus astronomicis recentihus et antiquis
ad examen mathematicum revocantur.^^ These
treatises exhibit much foresight and learning,
and were well calculated to effect the object for
which they were prepared, namely, to explode
false doctrines, and to demonstrate the only
rational hypothesis of our system.

Horrox next made some considerable improve-
ments in the lunar theory. It is generally
acknowledged, and indeed Sir Isaac Newton
expressly states, that this young philosopher
was the first person who discovered the moon's
motion to be in an ellipse about the earth, with
the centre in the lower focus. This discovery
was not merely an extended application of the
doctrines of Kepler. That great man had proved
the ellipticity of the orbit of Mars, the earth, and
other of the heavenly bodies, and had endeavoured
to explain its cause ; but Horrox, in his specu-
lation on the moon's motion, outstripped the
discernment of Kepler, inasmuch as he correctly
explained the physical cause of the curvilineal
motion of the planets, and shewed that it arises

26

from the joint action of two separate forces.
This was a great step in the progress of celestial
dynamics. He tells us that he had spent much
time in meditating upon the principle in virtue
of which the planets describe oval orbits, and that
he thought he had at length hit upon the true
theory. Kepler had supposed them to be whirled
round by the action of magnetic fibres, by which,
as he thought, a mutual influence was exercised
similar to that of the poles of loadstones ; but
being unable to reconcile the rotation of the
sphere upon its axis with this supposition, he
had recourse to the singular idea of the exterior
only of the planet being endued with rotatory
motion. Horrox states at some length his objec-
tion to this hypothesis, and having mentioned
difficulties which Kepler himself had not perceived,
he proceeds thus : "To say, as he doth, ^ Haec
contemporatio pertinet ad consilium creatoris,'
which I understand to be, so is the will of God,
if it had come sooner might have saved a labour
of all troublesome inquirys, for it is most true
that the will of God is the cause of all things, but
resting in generalitys is the death of philosophy.

27

I must have another cause of that ovall figure,
which it is most certain all the planets do affect.
This will not satisfy me." He then gives his own
views, and says that, as the laws of nature are
everywhere the same, there can be no doubt that
the true principle of the ellipse may be illustrated
by means of movements upon the surface of the
earth, as for example, the throwing of a stone into
the air, the rotation of which does not impede its
progress. In this analogy, to which he refers
more than once, we have the true explanation of
celestial motion, now understood to be the com-
bined effect of projective and attractive forces.
If a stone be thrown obliquely into the air, its
movement is governed by the impulse imparted
to it by the hand, together with the attractive
power of the earth. In obedience to these two
influences, instead of tending in its fall directly
towards the centre, it preserves whilst descending
the same angle at which it arose ; and if its pro-
gress were not interrupted by the earth's surface,
there is little doubt that it would revolve unceasing-
ly in an elliptical orbit with the centre in the lower
focus. Hence arises the general law. — When two

28

spheres are mutually attracted, if not prevented
by foreign influences, their straight paths are
deflected into curves concave to each other, and
corresponding with one of the sections of a cone,
according to the velocity of the revolving body.
Thus if a sphere were projected by an independent
power, as the planets were when launched forth
from the Creator's hand, it would move forward
in a right line for ever, unless attracted from it by
an extraneous force ; for instance, the earth would
preserve a perfectly straight course whilst per-
mitted to do so, but coming within the sun's
influence, it is induced to deviate from the
direction originally imj)ressed upon it. Now if
the velocity with which the revolving body is
impelled be equal to what it would acquire by
falling through half the radius of a circle described
from the centre of deflection, its orbit will be
circular ; but if it be less than that quantity, its
path becomes elliptical. This law was subse-
quently expanded by Sir Isaac Xewton into the
great principle of gravitation. As is well known,
he concluded that the power which causes a body
to fall to the earth, is of the same nature as that

29

which retains the planets in their orbits ; and he
pursued this discovery, until he finally evolved
an expression to which the phenomena of all the
celestial movements may be confidently referred.
Whilst thus engaged, he derived important assist-
ance from the writings of Horrox, who, by his
sagacious application of projectile to celestial
motion, has gained a distinguished place amongst
those whose labors have contributed to the
establishment of the true system of the universe.
Having ascertained the ellipticity of the moon's
orbit, and assigned its cause, he proceeded to
examine the various inequalities which render
the exact computation of her elements so difficult.
If she were not subject to any foreign influence,
the quantity of her ellipsis, the periods of her
revolutions, and other particulars would always
be the same ; but as she is attracted by the sun
as well as by the earth, the figure of her orbit is
altered, and irregularities are occasioned which
require to be corrected, in order that her theory
may be satisfactorily developed. Horrox's en-
quiries led him to a distinct knowledge of the
motion of the lunar apsides. He found that the

30

longer axis of the ellipse, or that imaginary
line which joins the apogee and perigee, moves
slowly round the centre of the earth in the same
direction as the moon revolves ; and this change
of position, which has since been ascertained to
amount to rather more than three degrees for
each of her sidereal revolutions, he rightly attributed
to the perturbative influence of the sun. The
beautiful experiment by which he illustrates this
phenomenon shews not only that he was perfectly
aware that an orbit might be formed by a central
force, but also that within certain limits the
heavenly bodies exercise a disturbing power upon
each other. Crabtree had asked to be favoured
with suggestions respecting the motion of the
aphelion of a planet. In reply, Horrox, always
adhering to his conviction of the harmony of
nature and the possibility of exemplifying celestial
movements by those which are common upon the
earth, supposes a ball to be suspended by a long
cord made fast to a hook in the ceiling. Now if the
ball be drawn from the perpendicular, and then
suddenly released, it oscillates for a while, with a
speed which increases as the centre is approached.

31

and diminishes when that point has been passed.
But, if after having been withdrawn from the
vertical, a tangential impulse be imparted, the ball
will describe an ellipse; and what is particularly to
be observed, the major axis will be seen slowly to
advance in the same direction with the ball,
performing, in course of time, a complete revolu-
tion. This illustrates the movement of the apsides
of the lunar orbit ; though in order to represent
nature more correctly, the centre of force should
be in the focus of ellipse, whereas in the experiment
it is in the centre. Horrox perceived this defect
in the illustration, and removed it by supposing
a slight breeze to blow continually in the direction
of the major axis, by which the relative situation
of the point at rest would be changed. This
ingenious experiment has been erroneously ascribed
to Hooke, who reproduced it at a meeting of the
Royal Society; but it was recorded as Horrox's
invention more than five-and-twenty years before
the idea was communicated to that learned
assembly : and as the doctrines exemplified are of
such importance, and were never before suggested
by any astronomer, it is very fitting that he should

32

have the credit of their discovery, and that the
time when they were first brought to light should
be correctly stated.

The principal irregularity affecting the place of
the moon in her orbit, next to the equation of the
centre, is usual called the evectioji, the existence
of which was known to the astronomers of Greece.
Its effect is to diminish the equation of the centre
when the line of the apsides Hes in syzigy, and to
increase it when it lies in the quadratures ; and
it was explained by Horrox, as depending upon
the libratory motion of the apsides, and the change
which takes place in the eccentricity of the lunar
orbit. This conclusion he arrived at from his own
observation before he was twenty years of age.

He also determined the value of the annual
equation, an inequality arising from the sun's
perturbative influence, and which under ordinary
conditions, is as the cube of his distance from the
earth. It varies according to the position of the
latter planet in its orbit as it approaches to, or
recedes from its primary. It was noticed both by
Tycho and Kepler, but neither of them assigned
its quantity. Horrox stated its maximum value

33

to be 11' 16" which is within four seconds of what
it has since been proved to be, by the most
accurate observations.

These improvements in the lunar theory, and

the various doctrines which he has illustrated in

connection with it, are alone sufficient to secure

for him a lasting reputation. Perhaps he is more

generally known by his other writings ; but this

is the subject in which his sagacity is the most

conspicuous, and with which his name is the most

honorably associated. Its accurate development

has from time to time occupied the attention of

the ablest astronomers ; but it is not too much to

say that his discoveries eclipsed the efforts of all

his predecessors, and have been the foundation of

the advancement towards perfection which has

been made in modern times. His views were

gradually unfolded in his letters to Crabtree, and

are partly embodied in a systematic treatise,

entitled ^'■Novce Theoiioe lunaris^ a Jeremid

Horroccio primum adinventce^ et 'postea in emen-

datiorem formam redacice, ex epistolis socii ijpsius

Gulielmi Crabtrei, ad eruditissimum virum Guliel-

mum Gascoignium scriptis^ explicatio,''''

34

Another instance of his sagacity consists in his
detection of the inequality in the mean motions
of Jupiter and Saturn. This phenomenon results
from the tangential impulse which is exercised to
a remarkable degree by these two planets upon
each other. It is a law of celestial mechanics that
action and reaction are equal and in contrary
directions, precisely as they are in reference to
terrestrial bodies. If an anvil be struck, the
reaction of the hammer is as great as the force
communicated by the blow ; and in like manner,
one planet cannot impart momentum to another
without subjecting itself to a corresponding in-
fluence. Consequently if the relative positions of
Jupiter and Saturn in their orbits are such that
the motion of one is accelerated, that of the other
will necessarily be retarded ; and a want of
uniformity arises which in the instance before us
is very important, on account of the extent to
which it accumulates. Thus about the time that
Horrox lived, and for a hundred and fifty years
before, the mean motion of Jupiter was constantly
increasing, and that of Saturn slackening; so
that, upon examining the Rudolphine tables, he

35

found that the calculated places of these planets
did not agree with their true situations. Accord-
ingly he suggested that the motion of Jupiter
might be corrected by adding 1° 30' to the
aphelion, and 2' to the mean longitude ; and he
estimated the quantity of acceleration at 1' in ten
years, which very nearly corresponds with the
increment actually given to the mean longitude
of Jupiter in each successive period of ten years
during the first half of the seventeenth century.
He also writes concerning the mean motion of
Saturn, that sometimes it appears to be singularly
retarded, and that in the time of Walther it was
evidently slower than Kepler's calculations had
made it ; and he proposes to subtract 4' from the
planet's mean longitude at the beginning of the
year 1600. He adds that the phenomenon would
occasion him greater annoyance were it not for
the consolation of his being in all probability the
first person to discover it ; and he requests
Crabtree to make frequent observations for the
purpose of finding out the correction to be applied
to the Rudolphine tables. From various remarks
which Horrox makes respecting the alteration in

D 2

36

the lengths of the periods of these two planets,
there is every reason to believe that he had
conjectured the inequality of their mean motion
to be periodic.

He bestowed considerable attention upon the
nature and movements of comets. These bodies
have at all times been regarded with gTeat interest;
not only by the ignorant, on account of their
sudden and terrific appearance as the supposed
harbingers of evil and the executioners of ven-
geance upon a guilty world, but equally by
the philosopher who has labored to explain
tlieir extraordinary physical constitution, the
irregularity of their movements, their apparent
variations in size, and other peculiarities. They
were for many ages believed to be only meteors
confined within the orbit of the moon. Tycho was
the first to refute this opinion by proving that they
travel beyond Mercury or Venus. Horrox pro-
cured his treatise upon comets, and, without entirely
adopting his suggestions, began to speculate upon
the elements of their orbits. His reflections at
different times shew how he advanced step by step
in search of truth, hissagaciousintellectlayinghold

37

of any outgrowth, and trying its strength to raise
him from one firm footing to another. At first he
conceived them to be projected from the body of
the sun in straight lines, an opinion previously
entertained by Kepler, and evidently suggested
by the prodigious elongation of their orbits. He
next assigned to them a velocity which diminishes
as they recede from the sun, and increases as they
return to it again. He then improved these
conjectures by supposing their path to be curvi-
lineal. Afterwards he says that they move "in an
elliptical figure or near it," and illustrates this
stage of his opinions by drawing a diagram for
the comet of 1577. The orbit which he traces
(see the figure) has an obtuse cusp at the sun,
and could not really have been described ; but it
shews that he had arrived at the conclusion that
comets revolve in curves returning into them-
selves. Wallis enclosed this diagram in a letter
to the Royal Society, requesting that it might be
carefully preserved, as it is in Horrox's own
handwriting. Finally he determines that comets
move " in elliptical orbits," being " carried round
the sun " with a " velocity which is probably

38

variable." This hypothesis has since been con-
firmed by a great number of observations, and is
now generally received. It was however reserved
for Neu'ton fully to determine the elements of
these bodies. He proved that any conic section
may be described about the sun, consistently with
the principle of gravitation ; and also that these
erratic bodies are subject to the general laws of
planetary motion, notwithstanding the elongation
of their orbits, and the unusual inclination of
their planes to that of the ecliptic.

Horrox also commenced a series of observations
on the tides. In his time very little was known
as to their physical cause. A^ there are no tides
in the Mediterranean, the ancients probably wrote
of them from representation. Kepler explained
their elevation more satisfactorily than any of his
predecessors. Horrox proposed to investigate the
subject thoroughly, and madevarious experiments
for the purpose of ascertaining the extent of their
rise and fall at different times, and at different
places, their direction, and the influences to which
various phenomena respecting them are to be
attributed. After he had continued his labors

39

for three months, he wrote to Crab tree, telling
him that he had noticed many interesting par-
ticulars which had not then been remarked by
any one, and that he hoped before long to arrive
at some valuable conclusions respecting their
nature and cause. Unfortunately we do not
possess the result of his observations, no papers
containing a systematic account of them having
come down to our times. We must however
allow him the credit of being the first person to
undertake a regular course of tidal observations,
for the purpose of philosophical investigation.

It is worthy of remark that he approved of,
and frequently employed a decimal system of
arithmetic. Since the commencement of the
seventeenth century, great improvements, most of
which are based upon the introduction of the
decimal principle, have been made towards
abridging the labour of calculation. This method
was invented by one Simon Steven, a native of
Bruges, in 1602, and it prepared the way for the
discovery of logarithms by Sir John Napier,
within twelve years afterwards. Horrox strongly
recommends the adoption of a decimal notation,

40

wherever it can be successfully applied ; and he
expresses his opinion that it would have been
better if the circle had been divided into 100 or
1000 parts, instead of 360. He says that such
an arrangement would have been preferable to
any other, and that the sexigesimal division is
attended with many inconveniences. He also
proposed to publish ephemerides in this form, in
order that astronomers might have an opportunity
of judging of its merits. Public attention in
England has of late years been particularly
directed to this subject, and much has been said
and written to prove that the application of the
decimal principle to our coinage would simplify
the course of exchange, and make the reckoning
of money more intelligible to every capacity; but,
admitting that such an alteration can only be
brought about by slow degrees, it is doubtful
whether the efforts that have been made for its
adoption, are at all commensurable with the ad-
vantages that would follow; and it does not lessen
our appreciation of Horrox's acuteness, to reflect
that he approved and employed a mode of cal-
culation which has yet to be introduced into
many departments of practical business.

41

Whilst he was studying the writings of Lans-
berg, he was led to conclude that there would be
a transit of Venus in 1639. The calculations of
the Flemish astronomer respecting the motions of
this planet are for the most part very inaccurate.
This obliged Horrox carefully to re-consider
them, and in so doing he discovered to his great
joy that the conjunction was to be expected. In
order to satisfy himself thoroughly upon this
interesting point, he consulted the Rudolphine
tables, by which his anticipations were confirmed.
Strange to say, it does not appear that Kepler had
any idea that a transit would take place in 1639 ;
for in a little work published at Leipsic in 1626,
entitled " Admonitiuncula ad Curiosos rerum
Ccelestium,'' he says, that Venus will pass over
the sun's disc in 1631, and not return thither
again until 1761. According to Hevelius no
transit was witnessed at the former date, and the
inaccuracy of the announcement may be traced
to the imperfect state of the Rudolphine tables.
Kepler died about twelve months before the time
at which it should have happened ; but Gassendi
sought for it at Paris, and although the sky was

42

clear, and he watched during the greater part of
three days, he did not see Venus in the body of
the Sun. The consequences of this mistake might
have been disastrous to the interests of science ;
for the assertion that there would be no transit
until 1761, had the effect of preventing astrono-
mers from looking out for that of 1639, which
took place on the 24th of November (Julian style)
as Horrox had calculated, and which but for his
foresight would not have been observed. It may
not be out of place to remark, that it is now
ascertained that the periods between the transits
of Venus are 8,235, 243, and 713 years ; so that
by adding any of these numbers to the date on
which some previous one is known to have
happened, the result gives the time when another
may possibly occur. There will be two more
transits of Venus, in the ascending node, during
the present century, viz.^ December 8th, 1874,
and December 6th, 1882, the latter of which will
be visible in this country. The observation is of
considerable value, as it affords means for correct-
ing the planet's elements, and for determining the
sun's horizontal parallax.

43

As soon as Mr. Horrox had satisfied himself as
to the time of the conjunction, he wrote to inform
his friend Crab tree that it was to be expected,
and requested that he would make what observa-
tion he could with his telescope, and especially
that he would carefully examine the planet's
diameter which, in his opinion, had been con-
siderably overestimated. He also begged him,
if time allowed, to communicate with Dr. Foster,
as it was desirable that the conjunction should be
observed in several places in order to prevent the
possibility of failure in case the heavens should
be overcast. His letter is dated, Hoole, October
26th, 1639, and he says — "My reason for now
writing is to advise you of a remarkable con-
junction of the Sun and Venus on the 24 th of
November, when there will be a transit. As
such a thing has not happened for many years
past, and will not occur again in this century, I
earnestly entreat you to w^atch attentively with
your telescope, in order to observe it as well as
you can. Notice particularly the diameter of
Venus, which is stated by Kepler to be 7\ and by
Lansberg to be 11', but which I believe to be

44

scarcely greater than 1'. If this letter should
arrive sufficiently early, I beg you will apprise
Mr. Foster of the conjunction, as, in doing so,
I am sure you would afford him the greatest
pleasure. It is possible that in some places the
sky may be cloudy, hence it is much to be desired
that this remarkable phenomenon should be
observed from different localities." He adds that
according to the Keplerian tables the conjunction
will be visible at Manchester at 8h. 8m. a.m.,
the latitude of the planet being 14' 10" south, but
that, according to his own correction, it should be
seen at 5h. 57m. p.m., with 10' south latitude. But
inasmuch as a slight change in Kepler's numbers
would considerably alter the quantity of the
planet's latitude, it would be desirable to watch
during the whole day, and also on the preceding
evening, and following morning, although he did
not doubt but that the transit would take place
on the 24th.

After having deliberated on the best method
of making the observation, he determined to
admit the sun's image into a dark room, through
a telescope properly adjusted for the purpose,

45

instead of receiving it through a hole in the
shutter merely, as recommended by Kepler. He
considered that by the latter method the delinea-
tion would not be so perfect, unless it were taken
at a greater distance from the aperture than the
narrowness of his apartment would allow ; neither
was it likely that the diameter of Venus would
be so well defined : whereas his telescope, through
which he had often observed the solar spots,
would enable him to ascertain the diameter of
the planet, and to divide the sun's limb with
considerable accuracy. Accordingly, having de-
scribed a circle of about six inches diameter upon
a piece of paper (see the plate), he divided its
circumference into 360 degrees, and its diameter
into 120 equal parts. This diagram was, in his
opinion, sufficiently large for all practical pur-
poses, nor did he think it necessary to carry the
subdivision further, as he could depend upon the
judgment of his eye with as much confidence as
upon any mechanical arrangement he could then
contrive. When the proper time came, he adjusted
his apparatus so that the image of the sun should
be transmitted perpendicularly to the paper, and

46

exactly fill the circle he had described. From
his own calculations he had no reason to expect
that the transit would take place, at the earliest,
before three o'clock in the afternoon of the 24th ;
but as it appeared from the tables of others that
it mio[ht occur somewhat sooner, in order to avoid
the chance of disappointment, he began to observe
about mid-day on the 23rd. Having continued
to watch wdth unremitting care for upwards of
four-and-twenty hours, excepting during certain
intervals of the next day when, as he tells us, he
was " called away by business of the highest
importance, which could not with propriety be
neojlected," he was at lens^th rewarded for his
anxiety and trouble by seeing a large dark round
spot enter upon the disc of light. This was
beyond doubt the commencement of the transit,
as the solar spots are very rarely spherical, and
do not consist of matter so regularly disposed,
nor so dense, especially about the edges, as the
object which he observed. They are generally
composed of an umbra, or dark space, which is
surrounded by a fainter shade. Venus could not
have presented this appearance, as her shadow

47

would be of an equal intensity of darkness and
of a circular shape. He therefore examined it
attentively, and arrived at some important con-
clusions. With respect to the inclination, he
found by means of a diameter of the circle set
perpendicularly to the horizon, the plane of the
circle being slightly sloped on account of the
sun's altitude, that to all appearance in the dark
chamber, the planet was wholly immersed by a
quarter past three, at about 62° 30', from the
vertex on the right hand, and that this inclination
continued constant until sunset. He also accu-
rately measured the distance of the Sun's and
Venus' centres at various times during the transit.
And he confirmed his previous conjectures
respecting the planet's diameter, inasmuch as it
only exceeded a thirtieth part of the diameter of
the sun by about one-fifth subdivision, so that
the proportion between them would be as 30' to
1' 12", or at least to 1' 20"; and this was evident
in every situation of Venus. Thus the observation
was well executed, and the results in all respects
such as he had anticipated. The inclination was
the only point upon which he was not quite

48

satisfied, as he was unable to estimate it with
very great exactness on account of the rapidity
of the planet's motion. Hevelius thinks he might
have used with advantage the method employed
in observing solar eclipses^ by which the sun's
image would have been prevented from going
beyond the paper, the apparatus having an
observatory circle and a small table fixed at the
end of the telescope, so that the most rapid
motion of the sun could not have disturbed
the observation ; but he forgets that even if
Horrox had thought of such a plan, his means
were probably too limited to allow of his procuring
the apparatus. The transit was witnessed at
Hoole, the little village before mentioned, of
which he was the curate. Its latitude is stated
to be 53° 35', and its longitude about 22° 30' from
the Fortunate Islands, or 14° 15' west of Urani-
burg.

AVith reference to the important business owing
to which, we have said, he was obliged to leave
his telescope, Hevelius further tells us, that he
would not have suff'ered his attention to have been
withdrawn by any occupation whatever, which

49

could have been undertaken at another time ;
but that he would have watched Venus more
assiduously than he had observed Mercury on a
previous occasion, and that he would never have
moved his eye from the circle unless some one
else had been ready to take his place. But
Horrox's absence is fully justified by the fact
that the business which called him away was the
discharge of his ministerial duties. Little calcu-
lation is necessary to prove that the 24th of
November 1639, old style, happened on a Sunday;
and the hours when he was obliged to relinquish
his occupation correspond with those at which
probably he would be engaged in conducting
divine service. The following extract in support
of this opinion will be read with interest It is
copied from one of Thomas Hearne's pocket books,
and dated February 8th, 1723 — '' Mr. Horrox, a
young man, minister of Hoole, a verypoorpittance,
within four miles of Preston, in Lancashire, was
a prodigy for his skill in astronomy, and had he
lived, in all probability, he would have proved
the greatest man in the whole w^orld in his
profession. He had a very strange unaccountable

E

50

genius, and he is mentioned with great honor by
Hevelius upon account of his discovery of Venus
in the Sun, upon a Sunday ; but being called
away to his devotions, and duty at church, he
could not make such observations, as otherwise
he would have done."

When Crabtree was informed of the expected
transit, he prepared to observe it in the same
manner as his friend. But he was not equally
successful; for though he watched most attentively,
the sky was so over-cast that the sun could not be
seen. At about 3h. 55m. by the clock, the clouds
suddenly cleared away, when to his delight he
saw Venus fully entered upon the Sun's disc.
Overcome with rapture, instead of improving the
opportunity thus favorably presented to him, he
stood gazing at the spectacle without using his
apparatus, nor did he recover his self possession
until the heavens were again obscured. This may
provoke a smile from those who know not the
overpowering emotion which attends success in a
painful and laborious pursuit; but let them
remember that such intervals of satisfaction are
the only reward which the astronomer receives for

51

his toils of mind and body, for his watchings by
night and by day, and for his tedious calculations
and patient study. Every inventor and discoverer
has his moments of ecstacy. When Pythagoras
had fairly demonstrated the great geometrical
truth, that the square described on the hypothe-
nuse of a right-angled triangle is equal to the
squares constructed upon the other two sides,
such was his exultation that he forthwith
sacrificed a hundred oxen to thegods; Archimedes,
having discovered a method of ascertaining the
specific gravity of difi*erent bodies, was so over-
joyed as to forget the proprieties of life. Thus
Crabtree is not the only person who has lost his
self-control in a moment of transport. Nor did he
entirely fail to take notice of what he saw ; for
though he was unable accurately to measure either
the distance of the centres, or the angle of inclina-
tion, he made a sketch from memory of the planet's
relative situation, which corresponded with what
Horrox had observed, and he estimated its
diameter at - of that of the sun. This observation
was made at Broughton, near Manchester, where
Crabtree resided, the latitude of which is 53° 24',

E 2

52

and the longitude 23° 15^ Horrox also apprised
his brother Jonas of the coming transit ; but the
unpropitious state of the weather prevented him
from profiting by the information. It is believed
that this phenomenon was not seen by any one
except the two friends ; and although the obser-
vation was made by both under unfavorable
circumstances, it has been of considerable advantage
to the science of astronomy. Horrox determined
the position of the nodes, and the elements of the
planet Venus with greater accuracy than had
hitherto been attained. He also found that the
time of the conjunction was 5h. 55m., instead of
5h. 57m. as he had anticipated ; that the planet's
latitude was 8' 31" south, instead of 10'; he
concluded that the nodes ought to be placed at
13° 22' 45" from Sagittarius and the Twins, rather
than 13° 31' 13" Avhere Kepler placed them; and
that of all the tables then in use, the Rudolphine
were the most exact.

It may not be out of place to insert here a
letter from Crabtree to Gascoigne, an able mathe-
matician, and the inventor of the micrometer, as
it refers to the observation, and is otherwise

53

interesting as shewing the friendship and esteem
which the writer felt for Horrox. After discussing
various theories respecting the spots on the sun,
and giving his opinion upon some philosophical
experiments, Crabtree says : —

" In the mean time let me encourage you to proceed
in your noble optical speculations. I do believe there are
as rare inventions as Gahleo's telescope yet undiscovered.
My Hving in a place void of apt materials for that purpose
makes me almost ignorant in those secrets : only what I
have from reason, or the reading of Kepler's Astronomia
Optica^ and Galileo. If you impart unto us any of your
optical secrets, we shall be thankful and obliged to you, and
ready to requite you in anything we can. It is true which
you say, that I found Yenus' diameter much less than any
theory extant made it Kepler came nearest, yet makes
her diameter five times too much. Tycho, Lansberg, and
the ancients about ten times greater than it should be.
So also do they differ as widely in the time of the con-
junction. By Lansberg the conjunction should have
been 16h. 31m. before we observed it : by Tycho and
Longomontanus 1 day 8h. 25m. before : by Kepler, who
is stiU the nearest the truth, 9h. 46m. before. So that
had not our own observations and study taught us a better
theory than any of these, we had never attended at that
time for that rare spectacle. You shall have the observa-

54

tion of it when we see you. The clouds deprived me of
part of the observation, but my friend and second self Mr.
Jeremiah Horrox, living near Preston, observed it clearly
from the time of its coming into the sun, till the sun's
setting ; and both our observations agreed, both in the
time, and diameter most precisely. If I can, I will bring
him along with Mr. Townley and myself to see Yorkshire
and you. You shall also have my observations of the
sun's last eclipse here at Broughton, Mr. Horrox's between
Liverpool and Preston, and Mr. Foster's in London.
Lansberg on eclipses, especially the moon, comes often
nearer the truth than Kepler, yet it is by packing together
errors ; his diameters of the sun and moon being false,
and his variation of the shadow being quite repugnant to
geometrical demonstration. His circular hypotheses, Mr.
Horrox, before I could persuade him, assayed a long time
with indefatigable pains and study to correct and amend ;
changing and turning them every way, still amazed and
amused with those lofty titles of perpetuity and perfection
so impudently imposed upon them ; until we found, by
comparing observations in several places of the orbes, that
his hypotheses would never agree with the heavens for all
times, as he confidently boasts ; no, nor scarce for any one
whole year together, alter the equal motion, prosthaphae-
resis, and eccentricity howsoever you will. Kepler's
ecliptick is undoubtedly the way which the planets
describe in their motions ; and if you have read his

55

commentary ' de motu Veneris/' and his ' Epitome
Astronomice Copernicce/ I doubt not you will say his
theor}^ is the most rational, demonstrative, harmonious,
simple, and natural that is yet thought of, or I suppose
can be ; all those superfluous fictions being rejected by
him, which others are forced so absurdly to introduce ;
and although in some respects his tables be deficient, yet
being once corrected by due observations, they hold true
in the rest, which is that argument of truth which Lans-
berg's and all others want. Your conceit of turning the
circle into 100,000,000 parts were an excellent one, if it
had been set on foot when astronomy was first invented.
Mr. Horrox and I have often conferred about it. But in
respect that all astronomy is already in a quite different
form, and the tediousness of reducing the tables of sines,
tangents, and all other things we should have occasion to
use into that form ; as also the inconveniences which we
foresaw would follow in the composing of the tables of
celestial motions, together with the greatness of the inno-
vation, deterred us from the conceit. Only we intend to
use the centesmes, and millesmes of degrees, because of
the ease in calculation. I have turned the Eudolphine
tables into degrees and millesmes, and altered them into a
far more concise, ready, and easy form, than they are done
by Kepler. My occasions force me to put an abrupt end
to my unpoHshed lines, and without more compliments,
to tell you plainly, but sincerely, I am your loving friend,
(though de facie ignotusj William Crabtree.

56

From my house in Broughton, near Manchester, this 7th
of August 1640." — The superscription of the letter is
"To his loving fiiend Mr. "WilKam Gascoigne, at his
father's house, in or near Leeds, Yorkshire."

It appeared desirable to Horrox, for many
reasons, that an account of the transit should be
prepared for the press, and accordingly he wrote
an elegant treatise entitled " Venus in sole visa^
seu tractatus Astronomicus^ de nohilissima solis
et Veneris conjunctione^ Novemhris die 24 Siyl,
Juliana mdcxxxix, autore Jeremia Horroxio^''
detailing the history of the observation and its
value to the interests of science. But not being
versed in the mysteries of authorship, and wanting
means, he was at a loss to know how to procure
its publication. He therefore requested Crabtree
to write to his bookseller who would probably be
able to advise them in this matter. After a few
letters had been interchanged without anything
satisfactory being concluded, he determined to
accept a long-standing invitation to visit his
friend at Broughton, which would enable him to
discuss the subject more freely, to confer upon
different points connected with their astronomical

57

pursuits, and more especially to give the right
hand of fellowship to one for whom he had so
hio-h a re2:ard. He had more than once before
purposed spending a few days with him, but his
intention had as often been frustrated by the
unsettled state of his affairs. At length, in order
to ^K some definite time, he ^vrote a letter from
Toxteth, dated 16th December 1640, in which he
arranged his journey for the 4th of January,
and told Crabtree that he might expect him on
that day, "if nothing unforeseen should occur."
This is the lano:uao;e of one who felt the uncer-
tainty of all human affairs, and was accustomed
to act as not knowing " what a day may bring
forth." His purpose was never carried into effect.
To the inexpressible grief of every true philosopher,
his short but brilliant career was closed by death
the day before he should have arrived at Brough-
ton. He expired on the 3rd of January 1641,
in the twenty-second year of his age. As the
flower of the morning falls before the scythe, so
was he cut off in the freshness and vigour of
youth. But his death was timely. His work
was done. He went to the grave in a full asre.

58

Having seen the glory of God afar off, his spirit
soared to the heaven of heavens to worship Him
as the centre of light and power. It is to be
regretted that the particulars of his decease are
nowhere recorded, and that we are left to mere
conjecture upon a point of so much interest ; but
there can be little doubt that whatever may have
been the immediate cause, his incessant labours
by night and by day materially contributed to
hasten it. Crabtree felt his loss acutely. His
rapid and comprehensive understanding had
removed many a difficulty from the path of
knowledge, his sympathy had lightened many
a toil. On the back of the letter last-mentioned,
which was found tied up with several others, was
the following touching inscription in Crabtree's
handwriting : —

" Letters of Mr. Jeremiah Horrox to me, of the years
1638, 1639, 1640, -until his death on the morning of the
3rd of Januar}', when he expired very suddenly, the day
before he had proposed coming to me. Thus God puts
an end to all worldly affairs ! and I am, alas ! bereaved
of my dearest Horrox. Irreparable loss ! Hence these
tears ! ''

The banishment of Tycho was overruled to the

59

advancement of astronomy, for it was owing to
this circumstance that Kepler obtained possession
of his theories and observations, which he after-
wards re-produced and improved w^ith such
advantage to the scientific world. But in the
remote part of the country in which Horrox died,
no one was found capable of appreciating the
value of his papers ; and consequently, instead of
being carefully preserved and kept together until
they could be revised with a view to publication,
many were destroyed, and the rest were carried
away to different places. Thus one portion of
them, which had been hastily concealed on account
of the troubles of the times, was discovered and
committed to the flames by a company of soldiers
who entered his father's house in search of
plunder. Another portion was appropriated by
his brother Jonas, who carried them over to
Ireland, where he died far from home and friends,
and the papers were never afterwards recovered.
A third fell into the hands of Jeremiah Shakerley,
and was made use of by him in the compilation
of the British tables published in the year 1653.
He subsequently went out to the East Indies ;

60

but before his departure entrusted his literary
effects to one Nathaniel Brooks, a London book-
seller, in whose possession they remained until
they were burnt in the great fire of September
1666. The only papers that escaped these disas-
ters were found in the house of Mr. Crabtree, who,
knowing their intrinsic merit, had claimed them
on the ground of past association ; and influenced
by motives of affection and esteem for their
author, had preserved them with the utmost fidelity.
It is not known how long this gentleman survived
his friend. There are a variety of statements
upon this point ; but the greater number of them
lead us to believe that he followed him to the
grave within a very few years. When his estab-
lishment at Broughton was broken up, and his
library about to be sold, these manuscripts,
including that of the Venus, were discovered by
Dr. John Worthington, Fellow of Emmanuel
College, Cambridge, a man of distinguished piety
and learning, who had been contemporary with
Mr. Horrox at the University. In a letter dated
28th of April 1659, addressed to Hartlib, who
had asked to see the dissertation on the transit,
he says : —

61

"I have, as you desire, sent you Mr. Horrox, his
discourse called " Venus in sole visa." Here are two
copies of it, but neither writ to the end. I lent them
some years since to a friend who promised out of both to
make out one, and then to print it ; but other business it
seems would not permit him to go through with the
work. In some other loose papers I perceive that the
author began his tract again and again (so curious was
he about it), but these seem to be his last, written with
his own hand. He lived at Toxteth Park near Liverpool,
in Lancashire, was some time of Emmanuel College,
Cambridge, admitted the same year I was. These papers
of his (with many others of astronomical observations) I
found in the study of one Mr. Crabtree (a Lancashire man,
and his great correspondent in these studies), and I bought
them after his death. By sending to some friend about
Liverpool or Toxteth, it may be known whether any of
Mr. Horrox's kindred have any of his papers.

'* Yours, &c.,

''J. WORTHINGTON."

Hartlib having obtained the manuscript of the
transit did not return it as soon as was expected.
This appears to have caused the doctor great
anxiety, and some little annoyance; for the
following year he wrote to desire that it might at
once be transcribed and sent back, as he did not

62

think there was another copy of it extant. He
also says, lest he should be thought uncourteous,
that, as intimated in his previous letter, it had
been borrowed on a former occasion by a person
who had professed a wish to publish it, a measure
which he entirely approved ; but he adds that
" all who design good things do not persevere
when it comes to a business of some labour." A
singular fatality seems to have attended these
papers, and to have fully justified the anxiety that
their owner had expressed concerning them ; for
while they were in Hartlib's possession, his study
was burnt down, and they were with difficulty
saved from destruction.

In the year 1660, a copy of the " Venus in sole
visa,'' possibly one of those which belonged to
Dr. Worthington, came into the hands of Huygens,
the Dutch astronomer, who having been asked by
Hevelius whether there was anything new going
on in the scientific world, said that he could
supply him with a copy of Horrox's celebrated
observation. Upon this announcement Hevelius
promised that if he would transmit it by the first
opportunity, it should be published with annota-

63

tions under cover with his account of the transit
of Mercury which was then nearly ready for the
press. After some delay it was forwarded ; and
when Hevelius received it, he expressed his
satisfaction that the two tracts were to be
made into one volume, in an eloquent strain :
" How greatly does my Mercury exult in the
joyous prospect that he may shortly fold within
his arms Horrox's long-looked for, and beloved
Venus. He renders you unfeigned thanks that
by your permission this much-desired union is
about to be celebrated, and that the writer is able
with your concurrence to introduce them both
together to the public." The annotations that
were appended are very voluminous, being of
greater length than the treatise itself They were
evidently written under unfavorable circumstances.
Their author was at the time overwhelmed with
affliction, and it is clear that they were somewhat
hastily drawn up ; for besides that they contain
errors which could not possibly have remained if
proper time had been allowed for revision ; the
work was out of the printer's hands in about three
months after Hevelius had received the manuscript

64

of the Venus, and a copy of it sent to Huygens
with an accompanying letter, dated May 1662, to
this effect : —

" YoTi have doubtless heard, much honored friend, of the
severe domestic calamity by which I was prevented from
more quickly fulfilling my promise ; and I am sure you wiU
not only readily excuse me, but sympathize with me in
this trial, when you understand how grievous an affliction
has befallen me. I have sent you by Dr. Peltrius my
Mercury produced amidst great mental anxiety, together
with Horrox's Yenus, happily risen for the pubHc good,
whilst alas ! my own beautiful Venus has set to my
infinite sorrow ! I pray you to consider them carefaUy,
untn I am able to send you something better. The
learned world is particularly indebted to you for bringing
Horrox's Venus to light, thus having cheerfully bestowed
a gift so excellent and acceptable as to demand the thanks
of the latest posterity. When you have read the book,
I beg you wiU give me your opinion of its merits, which
I shall esteem a great kindness, and in turn you wiU
always find me desirous of serving you."

To which Huygens replied on the25thof July 1662:

" Your most acceptable letter, and shortly afterwards
the volume of the new observations reached me safely,
and although I ought to have thanked you before for the
valuable gift, I have been so hindered that I could not

Q5

until now discharge this duty. The illustrious BuDialdus
informed me of the great affliction you have sustained by
the death of your dearest wife, on which account I feared
that this little work, which was then in hand, would be
delayed. But you have acted rightly in not suffering
your private loss to become a public misfortune ; for I
cannot say how highly astronomy is indebted to you for
so accurate a description of your beautiful observation.
Posterity cannot adequately repay you with its thanks.
Touching the posthumous work of Horrox now brought
to light, it is more satisfactory that it should have been
undertaken by you, than by me ; especially as you have
prepared an excellent and elegant edition, and increased
its value by a commentary. Furthermore, as you ask me
freely to give you my opinion of the several particulars
treated in the book, I frankly confess that your new
method of ascertaining the diameters of the planets by
that of Mercury appears less certain to me than to you."

The manuscript which was sent to Hevelius by
Huygens does not appear to have been returned
to him, as it is not among his papers in the public
library at Ley den.

It is remarkable that, in Hevelius' edition of
the Venus^ the name of the place where the
observation was made is nowhere to be found.
But this circumstance is not attended with any

F

66

difficulty, as tlie transit is described to have been
seen fifteen miles north of Liverpool, which
exactly corresponds with the situation of Hoole.
It is clear that Horrox was residing in this village
at the time of the conjunction, as all his letters
between the months of June 1639 and July 1640
are dated from thence ; and moreover the name
of the place is inserted in the catalogue of his,
observations. The work is now extremely scarce ;
there are probably not half a dozen copies of it in
the kingdom.

In February 1663, the subject of Horrox's
manuscripts was brought before the Royal Society,
and after some discussion, two of its members
were instructed to procure from Dr. Worthington
any papers which he possessed, for the purpose of
being revised and published at the society's ex-
pense. These were readily obtained, and were
entrusted to Dr. Wallis, the learned professor of
geometry at Oxford, who having been desired to
peruse them, reported upon their merits to the
society at considerable length. He said that he
and his colleague Dr. Christopher Wren had
attentively examined them, and that in their joint

opinion, what was written in Englisli, consisting
merely of notes from memory and unconnected
paragraphs produced at various times, was un-
suitable for publication ; but that they considered
the Latin pieces to be extremely valuable, and
well worthy of preservation. Wallis was hereupon
requested to gratify the learned world by digesting
and preparing such of the manuscripts as he
approved, a task which he gladly undertook, and
which he was admirably qualified to fulfil. The
plan that he adopted was as follows : By judici-
ously arranging the various tracts and dissertations
put into his hands by the society, including
especially those against Lansberg and Hortensius,
with others already mentioned, he compiled a
perfect treatise, entitled '' Astronomia Kepleriana
defensa et promotay This is divided into seven
disputations, with an introduction instituting a
comparison between the merits of Ptolemy, Co-
pernicus, Lansberg, Kepler, and others. The
first dissertation is upon various hypotheses, and
the formation of tables of the heavenly motions ;
the second upon the fixed stars ; the third upon
the obliquity of the Zodiac ; the fourth upon the

f2

68

semi-diameter of the sun ; the fifth upon the
diagram of Hipparchus ; the sixth upon the
movements of the stars ; and the seventh con-
tains an answer to the cavils of Hortensius against
Tycho. Whilst the manuscripts were in course
of preparation, several other papers and letters
were discovered, which were likewise carefully
collated, and printed by Wallis under the same
cover as those just enumerated. They consist of
extracts from Horrox's letters to his friend
Crab tree upon different astronomical subjects, a
catalogue of his observations, his new theory of
the moon, together with Flamsteed's lunar num-
bers upon it, also Crabtree's observations at
Broughton, and Flamsteed's treatise upon the
inequality of the solar year. The Astronomer
Eoyal himself explains the circumstances under
which his essay and numbers were appended to
this collection of Horrox's writings. In his
Autobiography, pubhshed some time ago by the
Admiralty, we read : —

"I made a journey into Lancashire, and called at
Townley, to visit Mr. Christopher Townley, who happened
to be then in London. But one of his domestics kindly

69

received me, and shewed me his instruments, and how his
micrometer was fitted to his tubes ; and from this time
forward we often conferred by letters. I procured Mr.
Gascoigne's and Mr. Crabtree's papers from him, and
Mr. Horrox's theory of the moon, to which he had begun
to fit some numbers ; but perfected none that I remember.
About this time Mr. Horrox's remains and observations,
having been collected by Dr. WaUis, were in the press.
I found his theory (of which a correct copy had fallen
into my hands) agree much better with my observations
than any other. Hereupon I fitted numbers to it, which
with an explanation of it were printed with his works.
Mr. CoUins advised me to print my discourse concerning
the equation of natural days with them : which I con-
sented to do ; and sent it up to him for that purpose
translated into Latin."

All these papers combine to form a quarto volume,
which was published at the expense of the Royal
Society. Wallis announced the completion of
his work in a letter to that learned body dated
September 21st, 1664, in which he informed them
that he had compared the different copies with
the originals, arranged the several subjects in
their proper places, and prefixed to the whole an
epistle dedicatory to their president, Lord Broun-

70

ker. A vote of thanks was then passed to Dr.
Wallis, and the printing of the book was next
referred to the consideration of the council ; but
owing to the low state of the society's funds at
this early period of its history, the volume was
not issued until nearly eight years afterwards.
Its publication is mentioned in a quaint letter
from John Collins to Dr. Edward Bernard,
written on —

" 16 March, 16-|-f^. From my house next the three
Crowns in Bloomsbury market. '^ He says, " Dr. WaUis,
his comment on the astronomicaU remaines of Horrox, is
to goe to the Presse here, and there is a new type
provided for the same, the Doctor desired to revise it
first, that he might adde a running title to the Topp, I
sent it on this day three weekes by Dobbins, Moores
coachman, giving notice to the Doctor thereof by the
Post and since wrote to the Doctor, but receiving no
answer am afeard the Doctor is by his disease iQcapacitated,
or under some great affliction."

The book at length made its appearance, being
entitled '-'•JeremiceHorrocciiAngli Opera Posthuma;
una cum Gul, Crabtrei observationibus coelestibus ;
necnon Joh. Flamstedii de temporis cequatione

71

diatriha numerisque lunarihus ad novum lunce
sy sterna Horroccii^'' printed in London, 1672.
In the years 1673 and 1678 it went tlirough two
fresh editions, but was so inaccurately revised
that the same typographical errors are found in
each ; for instance, the errata at the end have
been allowed to remain without correction, and
pp. 127 and 134 are reprinted by mistake 227
and 334. The book has become very valuable,
because so few copies of it are known to exist.
In one of Hearne's memoranda dated 1723, we
read, " Horrox's posthumous works were printed
by Wallis : they are now scarce. Mr. Whiteside,
of the Museum, bought them several years agoe
— but gave 75. 6 J. for them."

It has often been said to be a reflection upon
our country that the writings of Horrox should
have lain dormant for so long a time. As we
have seen, it was upwards of twenty years before
they were brought to light; and his beautiful
dissertation upon the transit of Venus made its
appearance in a foreign land. This was no doubt
owing in part to the troubled state of the times.
Political excitement and civil discord are not

72

favorable to the advancement of literature and
science. Moreover it should be remembered that
Horrox was then unknown to fame. He lived in
a remote part of the country, and died young.
As soon as the value of his papers had been
ascertained, measures were immediately adopted
for their security, and eventually for their pub-
lication. It would indeed have been better if
the account of the transit had been bound up
with the rest of his posthumous works, according
to the expressed wish of Flamsteed ; but it seems
that Wallis was under the impression at the time
that a distinct edition of the Venus was about to
be prepared by the Astronomer Royal, who was
believed to be in possession of an autograph
manuscript. No doubt he would willingly have
included it in the volume if some good reason
had not prevented him, for no one could have
shewn greater zeal for the honor of Horrox, nor
could have more deeply regretted that his
celebrated observations should have been so long
buried in obscurity. He says, "I cannot help
being displeased that this valuable observation,
purchaseable by no money, elegantly described,

73

and prepared for the press, should have lain hid
for two-and-twenty years, and that no one should
have been found to take charge of so fair an
offspring at its father's death, to bring to light a
treatise of such importance to astronomy, and to
preserve a work for our country's credit and for
the advantage of mankind." The complaint is
not entirely without foundation ; but it is at all
events a comfort to reflect that as soon as the
manuscripts were discovered, Horrox's fame was
endorsed by a society consisting of the most learned
of his countrymen, that his writings were printed
at public expense, and that his dissertation upon
the transit received a graceful recognition from
the leading astronomers of the continent of
Europe.

Besides the manuscripts already mentioned,
there are others of considerable interest, said to
have formerly belonged to Flamsteed, which are
now lodged in the library of the Greenwich
Observatory. Of these we may enumerate, —
Firstly, a transcript of the first twelve chapters
of the Venus in sole visa, being a small book six
inches high and four-and-a-half wide, containing

74

fifty-eight clearly written pages, the last of whicn
is not full, breaks off in the middle of the line,
and is followed by several blank leaves. The
account of the observations very nearly corres-
ponds with that given by Hevelius. There are
however no side-notes, a fact which confirms the
belief that those attached to the printed edition
formed no part of the original text. Although
this document bears no date, the time when it
was written may be concluded from a curious
circumstance which we must not omit to notice.
In the poem on the Telescope, inserted in the
middle of the second chapter, there are some
verses not to be found in the publication of
Hevelius :

" Et duplici nimium coelesti a fonte remoti
Tristia Satumi solatur lumina flamma."

Now Huygens first discovered a satellite of Saturn
in the year 1665 ; Cassini discovered a second in
October 1671, and a third in December 1672.
These lines are therefore evidently an interpola-
tion, since it was not known that Saturn had any
satellite until twenty-four years after Horrox's
death. They also prove that the manuscriptisnot of

75

much authority, as it could not have been written
for more than thirty years after the same event ;
and that although it belonged to Flamsteed, it
is not the autograph which he was beheved to
possess, and from which it was thought he in-
tended publishing a new and revised edition of
the Venus. It may however be used with ad-
vantage for suggesting improved readings, and
for making corrections in punctuation. — Secondly,
a manuscript upon half sheets of old foolscap,
ruled, and doubled so as to make a quarto eight
inches high and six wide, which consists of three
distinct parts, each paged separately, and headed
as follows : (1) " Jeremice Horroxii Proeludium
Astronomicmrij'' agreeing in substance with the
tract of a similar name already stated to have
been incorporated by Wallis, in the Opera
Fosthuma. Only the first book, " jDe Motu solis,''
has been commenced, having two chapters,
namely, one entitled " De parallaxi solis horizon-
tali,''^ and another " De refractio7ie solis et syderum.''
(2) " Astronomice Lanshergianoe censura^' a short
treatise, ending abruptly, the last line of which is
written as if it had been intended to be continued

76

on the following page. (3) ^^ JeremioB Horroxii
Astronomice Lanshergiancecensura etcum Kepleriana
Corrvparatio^' whicli contains the Prolegomena^ and
other pieces found in the printed works. Upon
comparing these two manuscripts with the Oj^era
Posthuma^ the general impression is, that they are
in many places less full than the published text.
Nevertheless they are extremely useful in throwing
light on obscure passages, and in enabling us to form
some idea of the manner in which Wallis arranged
his materials. They are both in the same hand-
writing, which is certainlybetter than Flamsteed's,
and totally different from his in character. They
were probably penned by a regular transcriber ;
and it may be concluded, therefore, that they are
of the same date. — Thirdly, an English manuscript
called Philosophical Exercises^ being a small book,
about the size of the Venus in sole visa^ divided
into two parts, namely : (1) A discussion re-
specting the elliptical motions of the planets, and
(2) Some more explicit rules upon the same
subject. The sun's parallax is treated of nearly
in the same way as that great question is discussed
in the papers printed by Wallis. Towards the

77

end there is " ^ New Theory of the Moon^' which
seems, from a comparison of the numbers em-
ployed, to have been the same as that adopted
by Flamsteed ; but this is only a conjecture, as
the latter part of the document is very incomplete.
This manuscript is evidently older than either of
the other two, nor is there anything against the
supposition of its having been written in the life-
time of Horrox. It is invested with pecuHar
interest, as being the only English composition of
his in existence ; and it is in general style more
hke an autograph than a transcription.

No monument was erected to the memory of
Horrox, nor any mark set over his grave, for
nearly two centuries after his death. In the year
1826, Mr. Holden, of Preston, delivered a course
of lectures upon astronomy in Liverpool, and
devoted the proceeds of one of his evenings to the
erection of a suitable tablet, which was placed in
St. Michael's Church, Toxteth Park. This was
a proof of his appreciation of the merits of Horrox,
and of his love for science ; and it was an act
which deserves general admiration. The monu-
ment is a handsome scroll of white marble,

78

mounted on a black slab, having the appropriate
representation of Venus crossing the Sun's disc,
beneath which is the following inscription :

Venus in sole visa. Nov. 24, 1639.

IN MEMORY OF

JEREMIAH HORROX, ONE OF THE GREATEST

ASTRONOMERS THIS KINGDOM EVER PRODUCED;

BORN IN TOXTETH PARK IN 1619;

DIED IN 1641, AGED 22.

HIS OBSERVATIONS WERE MADE AT HOOLE,

EIGHT MILES FROM PRESTON, WHERE HE

PREDICTED, AND WAS THE FIRST PERSON

WHO SAW, THE TRANSIT OF VENUS

OVER THE SUN.

THIS MONUMENT WAS ERECTED BY

M. HOLDEN, ASTRONOMER

1826.

But the name of Horrox is not commemorated in
his native place only ; it is no less so in the parish
of which he was a minister. The traditionary
remembrance of the young astronomer which still
exists at Hoole, began last year to assume a more
substantial form. The Rev. Mr. Brickel, the
present incumbent, naturally takes an interest in
his fame, and as his successor in office, felt
privileged to take measures for handing it down
to posterity. Occupying the same pulpit Sunday
after Sunday, he longed to identify Horrox with

79

the parish to the end of time, by raising a lasting
tribute to his memory. Hitherto there had been
no record of his connection with Hoole ; excepting
that upon the old Church clock and sun-dial
Horrox had inscribed the appropriate words " ut
hora, sic vita^"" and ^'- sine sole sileo,'^ calculated to
remind us of the shortness of life, and of our
helplessness until the " Sun of Righteousness
arise " upon the soul " with healing in His wings."
With this view Mr. Brickel addressed to the
gentlemen of influence in his neighbourhood, and
to various scientific men throughout the country,
a statement of the facts of the case, and asked
their sympathy and assistance. The learned gave
their testimony in favor of so distinguished a
member of their brotherhood, and men of high
position announced their readiness to contribute
in furtherance of so laudable an undertaking.
When sufficient funds were obtained, it was decided
that the Church should be beautified, and enlarged
by the erection of a chapel to be dedicated to the
memory of Horrox which should contain thirty
sittings free to the poor for ever. It was also
agreed that a memorial window should be placed

80

in it, together with a mural tablet having the
following inscription :

JEREMIAH HORROCKS

BORN AT LIVERPOOL, EDUCATED AT CA.MBRIDGE, THE CURATE

OF HOOLE,

DIED IN THE 22nd TEAR OF HIS AGE, 1641.

the wisdom of god in creation was his study from early youth !

fob his wonderful genius and scientific knowledge

men speak of him as

"one of England's most gifted sons,"

"the PRIDE and boast OF BRITISH ASTRONOMY."

amongst HIS DISCOVERIES ARE THE NEAREST APPROXIMATION TO THE

sun's PARALLAX.
IHE CORRECT THEORY OF THE MOON, AND THE TRANSIT OF VENUS.

BUT THE LOVE OF GOD IN REDEMPTION WAS TO HIM A YET NOBLEB THEME

THE PREACHING OF CHRIST CRUCIFIED A YET HIGHER DUTY J

LOVING SCIENCE MUCH, HE LOVED RELIGION MORE ;

AND TURNING FROM THE WONDERS OF CREATION TO THE GLORIES

OF THE CROSS, HE EXPRESSED THE EULE OF HIS LIFE

IN THESE MEMORABLE WORDS

^^ Ad majora avocatus, quce oh hcec parerga neglig non decuit."

IN MEMORY OF ONE

SO YOUNG AND YET SO LEARNED,

SO LEARNED AND YET SO PIOUS,

THIS CHURCH IN WHICH HE OFFICIATED,

HAS BEEN ENLARGED AND BEAUTIFIED.

This was accordingly done ; and the parish
authorities have replaced the old dial and time-
piece by a handsome clock, which is both an
ornament to the church, and a convenience to
the people. In this way the desire to do honor
to Horrox has been crowned with success ; and
we can only trust that the blessing of God may

81

rest upon the increased numbers who are now
enabled to worship in His sanctuary.

In estimating the attainments of this remark-
able young man, it must be remembered that we
possess only a small portion of his writings, the
bulk of them having unfortunately perished.
His published works are but a part of what he
wrote, and many of the tracts of which they are
composed were left in an unfinished state. Hence
some doctrines are treated systematically, whilst
others are introduced here and there as occasion
required. Omitting what might be inferred from
a general survey of his papers, it will be sufficient
for our purpose to mention such subjects only as
are discussed in regular order. We must remem-
ber also that since he lived, more than two
centuries have passed away, during which period
a number of men have arisen, by whose genius and
industry astronomy has been considerably de-
veloped. Our object is not to shew that he was
abreast with the learning of the nineteenth
century, but that he was greatly in advance of his
own times ; and that his exertions have in some
measure contributed to elevate the science to its

82

present proud position. The simple question to
be answered is: What has been the practical value
of his labors? What advantage were they to
those who came after him? In other words:
What has Horrox done for the improvement of
astronomy ?

The nature of his controversial papers has
already been explained. Their object was to
expose the vicious theories then prevailing, and to
disseminate rational and correct views respecting
the system of the universe. That his treatises
against Lansberg and Hortensius were well cal-
culated to eflfect this, there can be no doubt;
but unfortunately they remained so long in an
unpublished state that their usefulness was much
impaired. Twenty years is a period of great
importance in an era of progress. Nevertheless
these papers were not unserviceable ; as soon as
they were printed, they were read with great
interest, and passed through more than one
edition. His observation of the transit of Venus
was most valuable. No other person witnessed,
with anything like success, the transit of 1639.
By it he was enabled to correct the planet's

83

elements and to prove, contrary to the received
opinion, that her disc does not subtend an ano-le
greater than one minute. He also estimated the
sun's horizontal parallax more accurately than
any one who came before him : it had previously
been supposed to be at least two minutes, and
even Kepler had stated it at 57"; but Horrox
proved that it could not exceed 14", which was
within IJ" of the value assigned to it by Halley
sixty years afterwards. Horrox's reduction of
the sun's parallax is very remarkable ; for though
he had not diminished it enough, Newton in the
first edition of the Principia (1687) hesitated in
following him so far. He said " I am not quite
certain about the diameter of the earth as seen
from the sun. I have assumed it to be 40^
because the observations of Kepler, Riccioli, and
Yandelini do not allow of its being much greater.
The observations of Horrox and Flamsteed make
it somewhat less." He afterwards speaks of the
apparent diameter of the earth as " about 24", and
therefore the parallax of the sun would be about
12", very nearly as Horrox and Flamsteed had
determined. But the diameter would agree better

G 2

84

with the rule of this corollary if it were a little

larger" — ^^ quasi 24", adeoque jjarallcucis Solaris quasi
12", ut Horroccius et Flamstedius jpropemodum
statuere. Sed diameter paulo major melius congruat
cum regula hujus corollorariiy In the second
edition of the Principia (1713) all this is omitted,
and in a preceding corollary we read " the
parallax of the sun from the most recent observa-
tions is about 10''." In the third edition he
estimated it at 10^". When it is remembered
what expensive expeditions have been sent out
from our country for the purpose of observing
these transits, it is thought that the importance of
the observation, and the conclusions derived from
it will not seem to be over-rated. But as we have
intimated, his fame chiefly rests upon the improve-
ments he made in the lunar theory. His views
upon this subject have been received with gratitude
by the ablest astronomers. Newton's acknowledg-
ment that he was the first to discover the motion
of the moon to be in an ellipse about the earth,
with the centre in the lower focus, has been already
referred to ; the exact words in the Prin,cipia are
" Horroccius noster lunam in ellipsi circum terram.

85

in ejus umhilico inferiore constitutum, revolvi primus
statuit:'" and upon comparing the different editions
of the book, it will be seen that this statement
was added to the second, and retained in the third.
In his separate work, ''' De mundi systemate,'' he
speaks of Horrox's correction of the lunar theory
in terms of great admiration : " There are many
inequalities in the moon's motion not yet noticed
by astronomers. They are all deducible from our
principles, and are known to have a real existence
in the heavens. This may be seen in the hypo-
thesis of Horrox which is the most ingenious, and
if I do not deceive myself, the most accurate
of all : — in Horroccii Hypotfiesi ilia ingeniosissimd
et ni fallor omnium accuratissima videre licet.'"
Flamsteed declared his hypothesis for settling the
movements of the moon to be the most exact that
had ever been originated ; and he did not even
think it necessary to re-calculate the tables which
Horrox, for want of time, had not verified to his
own satisfaction. Halley, after speaking of the
theories of various eminent men^ says : *' but that
one alone of our Horrox which attributes to the
moon's orbit a libratory motion of the apsides, and

86

a variable eccentricity, seems to approach the
truth of nature ; for it represents the diameters
more agreeably to observation, and shews her
motion more accurately than any hypothesis
which I have hitherto seen." We may further
mention that Sir Isaac Newton largely availed
himself of Horrox's suggestions to explain the
general principles of perturbation, as laid down
in the 66th proposition of the first book of the
Principia. These improvements are so substantial
that there is no difficulty in ascertaining the
author to whom they are to be assigned. They
stand out as a landmark in the history of the
science. Taken in connection with his comments
upon the subject of planetary motion, they prove
that Horrox holds a prominent position amongst
those who have succeeded in developing that great
principle by which creation is held together. Few
men are permitted to originate, to confirm, and
to promulgate a great discovery. This is usually
the work of successive generations. Each master-
spirit pushes the enterprise a step further ; and
hence it is often difficult to decide who is fairly
entitled to the credit. The final elucidation may

87

be the result of an accumulated experience. The
ground is first broken up, then the seed is sown,
the tender plant is trained, and it grows and
thrives, until some one more fortunate than the
rest gathers the fruit. So it was with the principle
of gravitation, the discovery of which cannot be
wholly attributed to one man. It was, no doubt,
reserved for the transcendent genius of E^ewton
fully to define and to apply it ; but the existence
of such a power w^as known to others who came
before him ; and their ideas respecting it formed
part of the data from which he drew his sublime
conclusions. Thus Kepler had a considerable
knowledge of the subject, and many of his
conjectures have been substantiated. Dr. Gilbert
published similar doctrines in this country, and
gave them a more extended application. But
Horrox, by his explanation of the perturbative
influence of the sun, and by his illustration of
celestial and projectile motion, unfolded the theory
more completely than any of his predecessors.
He seems to have perfectly understood the identity
and universality of this unseen power ; for he
often tells us that the planets in their orbits are

88

affected by it in the same manner as bodies upon
the surface of the earth. His accurate views were
at length adopted by Newton, and made the
foundation of his philosophy. In proof of this
compare the following passages :

" Just as by the force of gravity a projectile might
describe an orbit, and revolve round the whole earth ; so
the moon, either by the force of gravity if it is endued
with gravity, or by any other force urging it towards the
earth, may be continually drawn thereto from a rectilineal
path, and turned into her present orbit ; and without sucli
a force she cannot be retained in her orbit. If the force
were less than it is, it would not cause her to deviate from
a rectilineal course sufficiently : if it were greater, it would
cause her to deviate too much, and draw her from her
orbit towards the earth. It is therefore required to be of
an exact amount ; and it is the business of mathematicians
to find the force which can accurately retain a body with
a given velocity in any given orbit ; and in like manner
to find the curvilineal path into which a body going forth
with a given velocity from any given place is turned from
its rectilineal way by a given force." — Newton Princijj,
Mathem. Bef. V.

"It is surely conceded by all that the motion of the
planetary bodies is neither perfectly circular, nor perfectly
uniform ; for observations shew, beyond dispute, that the

89

figure of the planetary orbits is elliptical or oval, and
different from a circle : and the motion of a body in this
ellipse is irregular being increased or diminished according
to its distance from the sun. Physical causes are not
wanting to shew that this movement is described by a
sort of geometrical necessity. We may satisfy ourselves
of the truth of this by an appeal to nature ; for as a
planet is moved by a magnetic impulse, why may not the
same principle be exercised in other ways ? A weight is
thrown into the air : at first it rises quickly, then moves
slowly, until at length it is stationary, and falls back to
the earth with a velocity which continually increases.
It thus describes a libratory movement. This movement
arises from the impetus in a right line which has been
imparted to it by your hand, together with the magnetic
influence of the earth, which attracts all heavy things to
itself, as a loadstone does iron. There is no need to dream
of circles in the air, and I know not what, when we have
the natural cause before our eyes ; and as regards the
motion of the planets which are subject to similar
influences, what reason, I ask, is there to barter an
explanation, the truth of which is comfirmed by so many
examples in nature, for a fictitious dream of circles?"
~Jer. Sot. Op. Fosth. Disp. VL Cap. I.

These paragraphs contain the same ideas express-
ed in different language. They both treat of the

90

physical cause of curvilineal motion, which is
explained to be the joint action of projectile and
attractive forces ; and they both speak of it as
pervading the planetary system, and illustrate it
by movements upon the surface of the earth.
Now as Sir Isaac Newton is known to have been
well acquainted with all that passed through
Wallis' hands, he must have seen Horrox's treatise
"D^ Mota Syderun^' from which the above extract
is taken ; and he tells us himself that he had read
his theory of the moon, in which the same princi-
ples are laid down. Without wishing to detract
from the merits of one who, as an astronomer,
has gained an immortal reputation, it is only right
that it should be known that some of the leading
doctrines upon which the philosophy of the
Principia is built were first propounded by Horrox.
Dr. Tatham in his " Chart and Scale of Truth,"
delivers his opinion upon this question in these
words :

" That every philosopher has an absolute right to avail
himself of the labors and discoveries of his predecessors,
as a legacy h'eely given him, is a privilege which
philosophy itself always claims. It is however a tribute

91

justly due to the memory of this extraordinary genius,
Mr. Horrox, whilst we regret the loss of many of his
valuable works, to acknowlege from what has been saved,
that he was principally instrumental in calling philosophy
out of the regions of fictitious invention, and putting her
on the investigation of the physical causes of things from
experiments and observations ; that he not only made the
applications of projectile motion to the analogical illustra-
tion of celestial, but also assigned the forces of projective
and attractive, on which all geometrical calculations are
founded ; and that, without injui'ing the immortal fame
of his great successor, he may be fairly considered the
forerunner of Newton/'

We may conclude these observations upon the
practical value of Horrox's labors by briefly
remarking that he was the first to predict and
observe the transit of Venus in 1639 ; to reduce
the Sun's parallax nearly to what it has since been
determined ; to discover the orbit of the Moon to
be an ellipse about the earth with the centre in the
lower focus; to explain the causes of orbital
motion ; to ascertain the value of the annual
equation with any degree of accuracy ; to devise
the beautiful experiment of the circular pendulum
for illustrating the action of a central force ; and

92

to commence a regular series of tidal observations
for the purpose of philosophical enquiry : besides
all which, he effected improvements in different
astronomical tables, recommended the adoption
of decimal notation, detected the inequality in the
mean motion of Jupiter and Saturn, and wrote his
opinions upon the nature and movements of comets.
That so much should have been achieved by so
young a man, notwithstanding many disadvantages,
may seem almost incredible ; but if there is one
fact connected with Horrox which, more than
another, rests upon incontrovertible evidence, it
is the age at which he died. This shews the lustre
of his genius, and imparts a melancholy interest
to his history. Those who have arrived at
distinction in intellectual pursuits have generally
done so early in life. Newton laid the foundation
of his greatest discoveries before he had attained
his thirtieth year ; Byron expired at thirty-six;
Pascal at thirty-nine ; Mozart at thirty -five ;
and Raphael at thirty-seven ; but Horrox's
years were fewer still ; they were not twenty-
two in number. Such being the case, it is
almost superfluous to say that he was gifted

93

with the highest mental qualifications. As an
instance of his extraordinary sagacity we may
mention his early appreciation of Kepler's works
which the philosophers who were contemporary
with Horrox could not understand. Riccioli,
Bouillaud, and others studied them to no purpose,
whereas he embraced them at once. He speaks of
Kepler as the " Prince of astronomers to whose
discoveries alone all who understand the science
will allow that we owe more than to those of any
other person : " he says that he venerates his
^' sublime and enviably happy genius, and if
necessary would defend to the utmost the
XJranian citadel of the noble hero who has so far
surpassed his fellows;" and he adds, ^' no one
while I live shall insult his ashes with impunity."
At the same time he took nothing upon trust, but
carefully examined every theory that was pro-
pounded. Thus he writes, " The calculations of
Lansberg and Longomontanus are false. Their
principles and numbers are false. Kepler's
hypotheses are true, and he seldom fails in his
numbers." He possessed a habit of self-reliance ;
and we often find him complaining of the servility

94

with which the astronomers of his day followed in
each other's track without verifying by observation
the doctrines that were handed down. In his
speculations upon physical causes he was never at
a loss for a new line of thought ; but if it did not
lead to a sound conclusion, it was dismissed as
readily as it had been called forth. His power of
reasoning out natural laws from the simple facts
of common experience deserves especial notice.
This is one of the greatest proofs of a philosophic
mind. It is in fact to see more than is apparent to
the common gaze. It enabled Newton to detect a
great principle in the fall of an apple ; and Gahleo,
whilst watching the swinging of a lantern in the
Cathedral Church of Pisa, to conjecture that the
oscillation of the pendulum might be turned to
important purposes as a measure of time. Horrox
beautifully expresses his belief in the harmony of
nature ; "Astronomy is natural and true. The sea
is agitated with the winds ; but the aether is clear
and open, without wind or any other resistance.
The bodies of the planets are solid and firm. Now
as a slinger aims accurately, and projects his
weapon with certainty, notwithstanding the re-

95

sistance of the air, why may not the heavenly
bodies, in like manner, rotate by an eternal
law ? " In short, Horrox possessed the spirit of a
true philosopher ; he was accustomed to generahze
facts, to weigh probabilities, and to take the most
ultimate -views ; and he improved to the utmost
his noble powers by his unwearied industry and
application. But scientific men are the most
capable of forming an opinion of his merits, and
to them we will appeal : Newton, and Foster of
Gresham College, speak of him as " a genius of the
very first rank ;" and Sir Isaac, anticipating the
publication of his works, expresses himself as '^glad
that the world will enjoy the writings of that
excellent astronomer Horrox." Ferguson alludes
to him as " our illustrious countryman ;" Brinkley
says that, had his life been spared, ^' his fame
would probably have surpassed that of all his
predecessors ; " Herschel calls him " the pride and
boast of British astronomy ; " Dr. Whewell, the
learned master of Trinity College, writes that,
"he has attempted to do him justice;" Lord
Brougham thinks that " nothing can be more clear
than the great merit of Horrox, and the severe

96

loss sustained by science from his early death ; "
Professor De Morgan says that " no monument is
needed for the name of Horrox, for wherever
Newton's Principia is known, there is his name
known also ; " and Professor Airy, the present
Astronomer Royal, ^' joins warmly " in admiration
of him. We will only add one more tribute to
his praise : Grant, in his learned treatise upon
physical astronomy, says that " Horrocks has
exhibited in his researches such sagacity of thought
and fertility of invention, such enlightened and
judicious views on the various subjects which
engaged his attention, and such unwavering-
confidence in the resources of his own mind,"
that, if he had remained on earth a few years
longer, " his name would have been a household
word for future generations."

Horrox was a poet as well as a philosopher.
The verses which he has introduced in his account
of the transit are very creditable, and evince a
bold imagination combined with a judicious taste.
They do not aim at being elaborate ; indeed, he
is so careless of detail, that by some his lines
would be considered unpolished. Had he been a

97

painter, his genius would have been impatient of
the restraint which is implied by the speciality of
arrangement found in the compositions of the
pre-Raphaelite school ; his ideas are strong and
clear, and roughly delineated, whilst his metaphor
somtimes borders upon exaggeration. But the
sentiment which pervades his verse is delicate and
refined. Enamoured of the heavens, he occasion-
ally chooses poetry because it is the best vehicle for
his passion ; but in his advances he never forgets
what is due to the society of the Muses. The
Pierian spring gushes forth with unusual force,
but its waters are always sweet and pure. His
performances are powerfully conceived, freely
executed, and are always in accordance with good
taste. It is not often that poetic fancy and ma-
thematical precision are so strongly developed in
the same mind.

But intellect is of no value unless sanctified by
grace. A man may be accounted a philosopher,
he may explain the laws of Nature more success-
fully than any of his predecessors ; but, if in his
investigations of natural phenomena, he sees
nothing but matter and motion, if he does not

H

98

recognize the power, the wisdom, andtheloveofHira
who creates and upholds, if he admires the work
without admiring the workman, he is a philosopher
"falsely so called." We are happy, therefore,
before concluding this Memoir, to be able to bear
testimony to Horrox's religious character. It is
true that he left no theological papers ; but this is
not to be wondered at, as he was only permitted to
exercise his ministration for so short a time.
But if he did not write in the capacity of a clergy-
man, he thought and believed as a Christian ; for
we find sentiments introduced even in his most
abstruse works, which show how much he lived
under the influence of religion. A few passages
in proof of this, besides those which have been
already quoted, may be adduced. When he was
about to enter upon the arduous task of correcting
the Rudolphine tables, he says : "And may He
who is the great and good God of astronomy,
and the conservator of all useful arts, bless my
unworthy efforts for His mercy's sake, and cause
them to redound to the eternal glory of His name,
and the advantage of mankind." In another
place he writes that he will not despair of further

99

discovery, "for I have been blessed by God's
grace with such success, that even now I have
something to be proud of." In his account of
the transit of Venus where he speaks of being
summoned, by his religious duties, from the
observation which he knew he should never again
have the opportunity of making, he draws a
contrast between the importance of things tem-
poral and things eternal which seems to express
the general rule of his life and conversation,
telling us that he was "called away to higher
duties, which must not be neglected for these
non-essentials." Would that this sentiment were
more deeply felt by all who are engaged in the
business of life ! These isolated passages shew
the spirit in which he did his work ; but one of
greater length has been preserved, where he speaks
expressly of his own religious opinions and con-
victions. It of course partakes of the fanciful
style of the schoolmen, and there is something
in a typical representation of the Deity from
which our more chastened thoughts necessarily
shrink ; but this fault belongs to the fondness for
conceit which then prevailed, and must not blind

H 2

100

us to the piety and humility of the writer. In
connection with some crude philosophical specu-
lations, we read: "I conclude that the eccentricity
of the planets is caused by the contention between
the suns magneticall (and always attractive)
virtue, and the planets dulnes naturally desiring
to rest unmoved, which dulnes, while the suns
circular motion carrys the planet from the aphe-
lium, is conquered, and so the planets motion
increaseth in fastnes ; but when the suns circular
revolution doth recarry it backe toward the
aphelium, the naturall torpor and dulnes in-
creaseth, by the presence and nearnes of that
place where it would rest.

" A right type may this be of mans dulnes to
good, which is the more by how much a man
more rests in himselfe, and is then onely quickned,
when the Spirit of God (like the rays of the sun)
doth draw our hearts, desirous to rest in them-
selves, and force them unwilling to follow Christ
(as the planets follow the suns circumvolution,
which begets a circular circumference), which
following is the onely cause of our comming neer
to god (as the suns circumference brings the

101

planets towards itselfe). All which agrees excel-
lently with that mysticall adumbration of the
thrise sacred trinity in (those poor types of God
as one calls them) round circles ; wher the father
(the center) doth beget the son (the circumfe-
rence) by efflux of the spirite (the rays). Keplers
astronomy differs from mine, as his religion :
He gives the planets a divers nature (good and
bad) that they may eyther come to the sun or fly
away at their pleasure, or at least (as his second
thoughts are) so dispose themselves (in spite of
all the suns magneticall power) that the sun is
bound to attract or expell them, according to that
position, which themselves defend against all the
suns labouring to incline the fibres. I, on the
contrary, make the planet naturally to be averse
from the sun, and desirous to rest in its owne
place, caused by a materiall dulnes naturally
opposite to motion, and averse from the sun,
without eyther power or will to move to the
sun of itselfe. But then the sun by its rays
attracts, and by its circumferentiall revolution
carrys about the unwilling planet, conquering
that naturall selfe rest that is in it, yet not so far

102

but that tlie planet doth much abate and weaken
this force of the sun, as is largely disputed afore.
So just do the papists, whose free will to good or
bad, can by its owne strength, go to God or fly
from him, or at least so frame their own actions,
as that God is bound to save them or damn them
volens nolens. But I will confesse myselfe not
equally composed of good and bad, that myselfe
may give eyther flesh or spirit the upper hand,
but rather wholly desirous to rest in my selfe,
wholly averse from God, and therefore justly
deserve (as the fixed stars jfrom the sun) to be
blown away from God in infinitum, but that God
by his Sons taking on him mans nature, and the
undeserved inspirition of his spirit, doth quicken
this dulnes, nay deadnes of my nature, yet still,
ah me ! how doth it choke and weaken those
operations ! If any one thinke aU this but an idle
conceit, I must tell him he doth too rashly deride
that booke of creatures, that voyce of the heavens
which is heard in all the world, and wherein
without question God hath instamped more mys-
terys than the lazy witts of men, more ready to
slight than amend any speculation, are ordinarily

103

aware of. Shall we thinke that he who was con-
tent to shadow out these mysterys with the poor
blood of buls and goats, will disdain to have them
typified in the more glorious bodys of the stars
and motions of the heavens ; which David ac"
counted such cleare Emblems of Gods glory
that he goes from speaking of the light of the
sun, unto Gods law, as if the subiect were still
the same, without any conclusion to the first, or
introduction to the latter. For my part I must
ever thinke that God created all other things, as
well as man, in his own image, and that the
nature of all things is one, as God is one, and
therefore an harmonicall agreeing of the causes of
all things, if demonstrated, were the quintessence
of most truly naturall philosophy.

Sic itur ad astra,
Repet hum : quicunque velit."

The curious illustrations in this extract will
easily be pardoned, when it is remembered that
they were in accordance with the phraseology of
the day. In later times, Wallis imagined that
the doctrine of the Trinity might be exemplified
by the three dimensions of a cube j and even the

104

theological treatises of the first half of the seven-
teenth century abound with expletives which
would now be considered unsuitable to the
solemnity of the subject. The passage breathes
sentiments of the purest piety, and it is gratifying
to know that Horrox had such clear views of
evangelical truth. The cause of religion is
strengthened when men of intellect range them-
selves on the Lord's side ; and the sneer of the
scoflfer is repressed, whose specious arguments
might otherwise unsettle the faith of the weaker
brethren, and throw poison into the waters of
life. How often do people take exception at
some statement of scripture because it appears
to them to be irreconcileable with the fresh dis
coveries of science; and although the point in
dispute may be comparatively unimportant, they
magnify its proportions, until the great principles
of the Bible are completely put out of sight :
whereas, by deferring their judgment for awhile,
it would be seen that such discoveries, if true in
themselves, are not opposed to the teaching of
Revelation. For it should be remembered that
all truth proceeds from one great source : it has

105

its foundation in the character of God. Science
and religion therefore can never be hostile to each
other ; because they both work up to a common
centre. The beneficence and order which are so
conspicuous in the constitution of the universe
were made known in the pages of scripture,
generations before the physical sciences were
cultivated. They are particularly conspicuous
in the plan of redemption. In this respect, the
arrangements of Providence resemble those of
Grace. At one time it was thought that the in-
equalities in the movements of the heavenly bodies
would prove fatal to the establishment of the
principle of gravitation ; instead of which, upon
further investigation, it was found, that so far
from being a violation of the general law, they
afforded a remarkable confirmation of it. In like
manner we read in the Gospel, that God can be
"just, and yet the justifier of him which believeth
in Jesus." This doctrine would not have been
deemed possible by the sages of old, and when
first preached, it was a stumbling-block to many ;
professing themselves to be wise they became
fools ; but a patient and unprejudiced examina-

106

tion convinces us that it is not only agreeable
to the perfections of God, but even throws a lustre
on His character, to which mankind before were
strangers. Religion and science then are only-
different departments of truth ; they can have no
conflicting interests. The subject of this Memoir
was eminent in the pursuit of both. He saw the
work of a Father's hand in the stars of heaven,
the flowers of the field, the cattle upon the hill-
side, the attributes of man, and in the rich
provision that has been made for every endangered
heir of glory. He knew that even the evil that
is in the world is a part of the general plan of
administration ; that sin is permitted to exist only
for the manifestation of a much more abounding
grace ; and that the present dispensation is intro-
ductory to one more perfect and more enduring,
when the irregularities which now perplex us
shall be seen to have been ordained in wisdom
and love. Thus whilst he took pleasure in
following up the path of discovery, and sought
to carry the line and compass to the utmost
boundaries of science, he was careful to study and
to practise beyond everything the laws of God's

107

spiritual kingdom, and thus to prepare for the
future world of light and happiness. In a word,
the greatest proof of his intelligence was, that he
lived and acted for Eternity.

" While yet on earth the youthful pastor trod,
He read the word and traced the works of God ;
The courses of the stars prophetic saw,
Unwound their order, and defined their law.
And yet a loftier view his eye could scan —
For this lost world salvation's glorious plan —
The firmament of souls redeemed from night,
The centre Jesus, and the circle light.
A Sage's love, a young Apostle's zeal,
The head to reason, and the heart to feel —
"With truth and mercy graced the preacher's tongue,
And o'er his life a holy radiance flung.
That meteor — life, soon lost to vision here,
Now shines unclouded in a glorious sphere ;
Yet here its light his bright example gives,
And here in fame undying Horrox lives."

OK

AN ASTRONOMICAL TREATISE

ON

THE CELEBRATED CONJUNCTION

or

VENUS AND THE SUN

On the 24th of November, 1639.

By JEEEMIAH HOREOX.

CHAPTER I.

The occasioUf excellence, and utility of the Observation.
Soon after the commencement of my astronomical
studies, and whilst preparing for practical observa-
tion, I computed the Ephemerides of several
years, from the continuous tables of Lansberg.
Having followed up the task with unceasing
perseverance, and having arrived at the point of
its completion, the very erroneous calculation of

no

these tables, then detected, convinced me that an
astronomer might be engaged upon a better work.
Accordingly I broke off the useless computation,
and resolved for the future with my own eyes to
observe the positions of the stars in the heavens ;
but lest so many hours spent on Lansberg should
be entirely thrown away, I made use of my
Ephemerides in ascertaining the positions of the
distant planets, so that I was enabled to predict
their conjunctions, their appulses to the fixed
stars, and many other extraordinary phenomena.
Delighted for the time with such a foretaste of
the science, I took great pains carefully to prepare
myself for further observation.

Whilst thus engaged, I received my first inti-
mation of this remarkable conjunction of Venus
with the Sun ; and I regard it as a very fortunate
occurrence, inasmuch as about the beginning
of October, 1639, it induced me, in expectation
of so grand a spectacle, to observe with increasd
attention. I pardon, in the meantime, the
miserable arrogance of the Belgian astronomer,
who has overloaded his useless tables with such
unmerited praise, and cease to lament the misap-

Ill

plication of my own time, deeming it a sufficient
reward that I was thereby led to consider and
to foresee the appearance of Venus in the Sun.
But on the other hand, may Lansberg forgive
me that I hesitated to trust him in an observation
of such importance ; and, from having been so
often deceived by his pretension to universal
accuracy, that I disregarded the general reception
of his tables. Besides, I thought it my duty to
consult other calculations, especially those of
Rudolphi, which Hortensius has vainly labored
to depreciate. Daily experience indeed convinces
me that what Lansberg says (whether with less
modesty or truth I know not) of his own tables
may be affirmed with propriety of Kepler's,
namely, that they are superior to all others.

" Quantum lenta solent inter viburna cupressi."

The more accurate calculations of Rudolphi
very much confirmed my expectations; and I
rejoiced exceedingly in the hope of seeing Venus,
the rarity of whose appearance in conjunction
with the Sun had induced me to pay less attention
to the more common phenomena of the same kind

112

visible in tlie planet Mercury ; for though hitherto
these phenomena have been observed on one
occasion only, the science of astronomy holds out
to us the assurance that they will, even in our
time, frequently appear.

But lest a vain exultation should deceive me,
and to prevent the chance of disappointment, I
not only determined diligently to watch the
important spectacle myself, but exhorted others
whom I knew to be fond of astronomy to follow
my example; in order that the testimony of
several persons, if it should so happen, might the
more effectually promote the attainment of truth ;
and because by observing in different places, our
purpose would be less likely to be defeated by the
accidental interposition of the clouds or any
fortuitous impediment.

The chance of a clouded atmosphere caused me
much anxiety ; for Jupiter and Mercury were in
conjunction with the Sun almost at the same time
as Venus. This remarkable assemblage of the
planets, (as if they were desirous of beholding, in
common with ourselves, the wonders of the
heavens, and of adding to the splendour of the

113

scene), seemed to forebode great severity of
weather. Mercury, whose conjunction with the
Sun is invariably attended with storm and tempest,
was especially to be feared. In this apprehension
I coincide with the opinion of the astrologers,
because it is confirmed by experience; but in
other respects I cannot help despising their more
than puerile vanities.

I have thought it right, independently of the
remarks upon the planets which I have elsewhere
made, to publish a separate treatise upon this
observation, on account of its great practical
utility and excellence above all others, which I
trust I may be permitted to set forth without
being accused of ostentation.

In the first place, I found that it was well suited
to correct the mean motion of Venus, on account
of two advantages which other observations do
not possess.

The one consists in the difiiculty which might
be occasioned by the parallax of the orbit; or the
second equation, being removed from this obser-
vation. I speak in accordance with the opinion of

I

114

Copernicus, whom alone I shall follow in his
general hypotheses. The conjunction placing the
bodies of the sun, of the earth, and of the planet
herself in one line has removed all possibility of
deception from a spectacle which in other positions
presents difficulties scarcely possible to overcome.

The other advantage results from the proximity
of Venus to the earth, and her convenient situa-
tion as respects the sun, whence it happens
that one minute in her longitude alters her
apparent situation nearly three minutes. If
therefore on the other hand, we can observe
her apparent place within a minute, it is clear
that we shall ascertain her real longitude in her
orbit within the third part of a minute ; whereas
when the planet is in other situations, a whole
degree scarcely affects the apparent place of her
longitude, especially in her greatest distances from
the sun, when observations of her are most fre-
quently and correctly made ; moreover both these
and other observations plainly prove that the
mean motion of Venus has never yet been de-
termined by astronomers with sufficient accuracy.

In the second place, no other observation shews

115

so correctly the longitude of the node of Venus j
for the telescope which I employed on this
occasion is much more accurate than those gene-
rally used. Neither have I depended altogether
upon the latitude of the fixed stars, with regard
to which there might be some doubt, but have
calculated from the sun itself, which is always
necessarily fixed in the Ecliptic. Moreover there
is an additional circumstance in the very great
visible inclination of the orbit, by which, the
apparent latitude being rapidly changed, the
distance of Venus from the node is more minutely
ascertained; one minute of observed latitude
determining the longitude of the node to the tenth
part of a degree ; upon this point, however, it is
right to add that modern astronomers are divided.
But especially would I call the attention of the
reader to the surprising minuteness of Venus'
apparent diameter; even though Gassendi has
already bespoken the admiration of astronomers,
by pointing out a similar peculiarity with respect
to Mercury; and though I am not the first to
notice this circumstance, I can at all events con-
firm it. By another and a very striking proof it

i2

116

will be seen how much we are liable, in estimating
the diameters of the planets, to be deceived by
their refraction.

Influenced by these reasons, and following the
example of Gassendi, I have drawn up an account
of this extraordinary sight, trusting that it will
not prove less pleasing to astronomers to contem-
plate Venus than Mercury, though she be wrapt
in the close embraces of the sun ;

YincKsque nova ratione paratis
Admisisse Deos.

Hail! then, ye eyes that penetrate the inmost
recesses of the heavens, and gazing upon the
bosom of the sun with your sight-asissting tube,
have dared to point out the spots on that eternal
luminary! And thou too, illustrous Gassendi,
above all others, hail ! thou who, first and only,
didst depict Hermes' changeful orb in hidden
congress with the sun. Well hast thou restored
the fallen credit of our ancestors, and triumphed
o'er the inconstant Wanderer. Behold thyself,
thrice celebrated man ! associated with me, if I
may venture so to speak, in a like good fortune.
Contemplate, I repeat, this most extraordinary

117

phenomenon, never in our time to be seen again !
the planet Venus drawn from her seclusion,
modestly delineating on the sun, without disguise,
her real magnitude, whilst her disc, at other times
so lovely, is here obscured in melancholy gloom ;
in short, constrained to reveal to us those impor-
tant truths, which Mercury, on a former occasion,
confided to thee.

How admirably are their destinies appointed !
How wisely have the decrees of Providence
ordered the several purposes of their creation !
Thou, a profound Divine, hast honored the patron
of wisdom and learning ; whilst I, whose youthful
days are scarce complete, have chosen for my
theme the Queen of love, veiled by the shade of
Phoebus' light I

CHAPTEE II.

Account of the Observation.
Whilst I was meditating in what manner I should
commence my observation of the planet Venus so

118

as effectually to realize my expectations, the recent
and admirable invention of the telescope afforded
me the greatest delight, on account of its singular
excellence and superior accuracy above all other
instruments. For although the method which
Kepler recommends in his treatise on Optics,
of observing the diameter and eclipses of the
sun through a plain aperture without the aid
of glasses, is very ingenious, and in his opinion,
on account of its freedom from refraction, pre-
ferable to the telescope; yet I was unable to
make use of it, even if I had wished to do
so, inasmuch as it does not shew the sun's image
exactly, nor with sufficient distinctness, unless
the distance from the aperture be very great,
which the smallness of my apartment would
not allow. Moreover I was afraid to risk the
chance of losing the observation ; a misfortune
which happened to Schickard, and Mogling, the
astronomer to the Prince of Hesse, as Gassendi
tells us in his Mercury: for they, expecting to
find the diameter of Mercury greater than it was
reasonable to anticipate, made use of so large an
aperture that it was impossible to distinguish the

119

planet at all, as Schickard himself has clearly
proved ; and even though Venus gave promise of
a larger diameter, and thereby in some measure
lessened this apprehension, and I was able to
adapt the aperture to my own convenience, yet in
an observation that could never be repeated, I
preferred encountering groundless fears to the
certainty of disappointment. Besides, I possessed
a telescope of my own of such power as to shew
even the smallest spots upon the sun, and to
enable me to make the most accurate division of
his disc; one which, in all my observations, I
have found to represent objects with the greatest
truth. This kind of instrument therefore I
consider ought always to be preferred in such
experiments. As soon as its usefulness became
known to me, I eulogized it in the following lines :

Divine the hand which to Urania's power

Triumphant raised the trophy, which on man

Hath first bestowed the wondrous tube by art

Invented, and in noble daring taught

His mortal eyes to scan the furthest heavens.

Whether he seek the solar path to trace,

Or watch the nightly wanderings of the moon

120

"WTiilst at her fullest splendour, no such guide

From Jove was ever sent, no aid like this

In brightest light such mysteries to display ;

Nor longer now shall man with straining eye

In vain attempt to seize the stars. Blest with this

Thou shalt draw down the moon from heaven, and give

Our earth to the celestial spheres, and &s.

Each orb in its own ordered place to run

Its course sublime in strict analogy.

For whilst thou see'st the lunar disc display

Such rocks and ocean-depths unfathomable.

What powers prevent thy sight of worlds celestial

From tracing all their semblance to this earth ?

This hand divine, right bold Copernicus,

Supplies fresh arms to vindicate thy cause,

Supporting thee who dared to make the worlds

Eevolve by laws unchangeable, it clothes

The hosts of heaven with earthly forms, and bids

The earth itself to claim the second place

Below the sun, a rival to the stars

That hold their stations in the realms of space.

Forbidding more the senseless crowd to rule

O'er minds whose high-aspiring thoughts shall soon

Surpass the utmost bounds of ancient lore.

Its powers disperse the troop that know no rule

But texts too vainly taught by him who gave

Such lasting honors to Stagira's name ;

121

They tear to shreds a thousand fancied laws
That truth deface like spots upon the sun,
And send the tomes that else might lead astray
A fitting present to the moths and worms.
This prjdng tuhe too shews fair Venus' form
Clad in the vestments of her borrowed light,
"While the unworthy fraud her crescent horn
Betrays. Though bosomed in the solar beams
And by their blaze o'erpowered, it brings to view
Hermes and Venus from concealed retreats ;
With daring gaze it penetrates the veil
Which shrouds the mighty ruler of the skies,
And searches all his secret laws. 0 ! power
Alone that rivalest Promethean deeds !
Lo, the sure guide to truth's ingenuous sons !
Where'er the zeal of youth shall scan the heavens,
0 may they cherish thee above the bHnd
Conceits of men, and the wild sea of error
Learning the marvels of this mighty Tube !

Having attentively examined Venus with my
instrument, I described on a sheet of paper a
circle whose diameter was nearly equal to six
inches, the narrowness of the apartment not
permitting me conveniently to use a larger size.
This however admitted of a sufficiently accurate
division; nor could the arc of a quadrant be

122

apportioned more exactly, even with a radius of
fifty feet, which is as great an one as any astrono-
mer has divided; and it is in my opinion far
more convenient than a larger, for although it
represents the sun's image less, yet it depicts it
more clearly and steadily. I divided the
circumference of this circle into 360° in the
usual manner, and its diameter into thirty
equal parts, which gives about as many minutes
as are equivalent to the sun's apparent diameter :
each of these thirty parts was again divided
into four equal portions, making in all one
hundred and twenty; and these, if necessary,
may be more minutely subdivided; the rest I
left to ocular computation, which, in such small
sections, is quite as certain as any mechanical
division. Suppose then each of these thirty parts
to be divided into 60", according to the practice
of astronomers. When the time of the observation
approached, I retired to my apartment, and
having closed the windows against the light, I
directed my telescope, previously adjusted to a
focus, through the aperture towards the sun and
received his rays at right angles upon the paper

VENUS ON THE SUN'S DISC.

"irENvs

123

already mentioned. The sun's image exactly
filled the circle, and I watched carefully and
unceasingly for any dark body that might enter
upon the disc of light.

Although the corrected computation of Venus'
motions which I had before prepared, and on the
accuracy of which I implicitly relied, forbad me
to expect anything before three o'clock in the
afternoon of the 24th ; yet since, according to the
calculations of most astronomers, the conjunction
should take place sooner, by some even on the
23rd, I was unwilling to depend entirely on my own
opinion which was not sufficiently confirmed, lest
by too much self-confidence 1 might endanger the
observation. Anxiously intent therefore on the
undertaking through the greater part of the
23rd, and the whole of the 24th, I omitted no
available opportunity of observing her ingress.
I watched carefully on the 24th from sunrise to
nine o'clock, and from a little before ten until
noon, and at one in the afternoon, being called
away in the intervals by business of the highest
importance which, for these ornamental pursuits,
I could not with propriety neglect. But during

124

all this time I saw nothing in the sun except a
small and common spot, consisting as it were of
three points at a distance from the centre towards
the left, which I noticed on the preceding and
following days. This evidently had nothing to
do with Venus. About fifteen minutes past three
in the afternoon, when I was again at liberty to
continue my labors, the clouds, as if by divine
interposition, were entirely dispersed, and I was
once more invited to the grateful task of repeating
my observations. I then beheld a most agreeable
spectacle, the object of my sanguine wishes, a
spot of unusual magnitude and of a perfectly
circular shape, which had already fully entered
upon the sun's disc on the left, so that the limbs
of the Sun and Venus precisely coincided, forming
an angle of contact. Not doubting that this was
really the shadow of the planet, I immediately
applied myself sedulously to observe it.

In the first place, with respect to the inclination,
the line of the diameter of the circle being
perpendicular to the horizon, although its plane
was somewhat inclined on account of the Sun's
altitude, I found that the shadow of Venus at the

125

aforesaid hour, namely fifteen minutes past three,
had entered the Sun's disc about 62° 30', certainly
between 60° and 65% from the top towards the
right. This was the appearance in the dark
apartment ; therefore out of doors beneath the open
sky, according to the law of optics, the contrary
would be the case, and Venus would be below
the centre of the sun, distant 62° 30' from the
lower limb, or the nadir, as the Arabians term it.
The incUnation remained to all appearance the
same until sunset^ when the observation was
concluded.

In the second place, the distance between the
centres of Venus and the Sun I found, by three
observations, to be as follows : —

The Hour. Distance of the Centres.

At 3 . 15 by the clock. 14' 24-
„ 3.35 „ 13' 30"

„ 3.45 „ 13' 0"

„ 3 . 50 the apparent sunset.
The true setting being 3.45. and the apparent
about 5 minutes later, the difi*erence being caused
by refraction. The clock therefore was sufficiently
correct.

126

In the third place, I found after careful and
repeated observation, that the diameter of Venus,
as her shadow was depicted on the paper, was
larger indeed than the thirtieth part of the solar
diameter, though not more so than the sixth, or
at the utmost the fifth, of such a part Therefore
let the diameter of the Sun be to the diameter of
Venus as 30' to V 12". Certainly her diameter
never equalled V 30", scarcely perhaps 1' 20", and
this was evident as well when the planet was
near the Sun's limb, as when far distant from it.

This observation was made in an obscure
village where I have long been in the habit of
observing, about fifteen miles to the north of
Liverpool, the latitude of which I believe to be
53° 20', although by the common maps it is stated
at 54° 12', therefore the latitude of the village
will be 53° 35', and the longitude of both 22° 30'
from the Fortunate Islands, now called the
Canaries. This is 14° 15' to the west of Urani-
burg in Denmark, the longitude of which is
stated by Brahe, a native of the place, to be
36° 45' from these Islands.

This is all I could observe respecting this cele-

127

brated conjunction, during the short time the
Sun remained in the horizon : for although Venus
continued on his disc for several hours, she was
not visible to me longer than half-an-hour, on
account of his so quickly setting. Nevertheless,
all the observations which could possibly be made
in so short a time, I was enabled, by Divine
Providence, to complete so effectually that I
could scarcely have wished for a more extended
period. The inchnation was the only point upon
which I failed to attain the utmost precision ; for,
owing to the rapid motion of the Sun, it was
difficult to observe with certainty to a single
degree, and I frankly confess, that I neither did
nor could ascertain it. But all the rest is suffi-
ciently accurate, and as exact as I could desire.

CHAPTER III.

What others observedy or might have observed, of this
Conjunction.

When first I began to attend to this Conjunction,
I not only determined myself to watch diligently
an appearance so important, but invited others

128

also whom I knew to be interested in astronomy
to do the same, in order that the testimony of
many observers, should it so happen, might more
firmly establish the truth ; and especially because,
if observations were made in different places, our
expectations would be less likely to be frustrated
by a cloudy sky or any other obstacle. I wrote
therefore immediately to my most esteemed friend
William Crabtree, a person who has few superiors
in mathematical learning, inviting him to be
present at this Uranian banquet, if the weather
permitted ; and my letter, which arrived in good
time, found him ready to oblige me; he therefore
carefully prepared for the observation, in a
manner similar to that which has been mentioned.
But the sky was very unfavorable, being obscured
during the greater part of the day with thick clouds;
and as he was unable to obtain a view of the
Sun, he despaired of making an observation, and
resolved -to take no further trouble in the matter.
But a Httle before sunset, namely about thirty-
five minutespast three, certainly between thirty and
forty miuntes after three,the Sun bursting forth
from behind the clouds, he at once began to

129

observe, and was gratified by beholding the
pleasing spectacle of Venus upon the Sun's disc.
Rapt in contemplation, he stood for some time
motionless, scarcely trusting his own senses,
through excess of joy ; for we astronomers have
as it were a womanish disposition, and are overjoyed
with trifles and such small matters as scarcely
make an impression upon others ; a susceptibility
which those who will may deride with impunity,
even in my own presence, and, if it gratify them,
I too will join in the merriment. One thing I
request : let no severe Cato be seriously offended
with our follies; for, to speak poetically, what
young man on earth would not, like ourselves,
fondly admire Venus in conjunction with the
Sun, " pulchritudinem divitiis conjunctam " ?
But to returUj he from his ecstacy, and I from
my digression. In a little while, the clouds again
obscured the face of the Sun, so that he could
observe nothing more than that Venus was cer-
tainly on the disc at the time. What he actually
saw in so short a space was as follows :

In the apartment, Venus occupied the right
side of the Sun, being higher than its centre,

K

130

and therefore in the heavens lower and on the left.
She was distant at the aforesaid hour, namely
thirty-five minutes past three, a sufficiently appre-
ciable space from the Sun's left limb ; but
Crabtree's opportunity was so limited that he
was not able to observe very minutely either the
distance itself, or the inclination of the planet.
As well as he could guess by his eye, and to the
best of his recollection, he drew upon paper the
situation of Venus, which I found to differ little
or nothing from my own observation ; nor indeed
did he err more than Apelles himself might have
done in making so rapid a sketch. He found the
diameter of Venus to be seven parts, that of the
Sun being two hundred, which, according to my
calculations, gives about 1' 3".

This observation was made near Manchester,
called by Antoninus Mancunium or Manucium,
the latitude of which Mr. Crabtree makes 53° 24',
and the common tables 45° 15' ; the longitude
23° 15', or three minutes of time to the east of
Liverpool, from which it is distant twenty-four
miles.

I wrote also of the expected transit to my

131

younger brother, who then resided at Liverpool,
hoping that he would exert himself on the occasion.
This indeed he did, bat it was in vain ; for on
the 24th, the sky was overcast, and he was unable
to see anything, although he watched very care-
fully. He examined the Sun again on the
following day which was somewhat clearer ; but
with no better success, Venus having already
completed her transit.

I hope to be excused for not informing other
of my friends of the expected phenomenon,
but most of them care little for trifles of this
kind, preferring rather their hawks and hounds,
to say no worse ; and although England is not
without votaries of astronomy, with some of
whom I am acquainted, I was unable to
convey to them the agreeable tidings, having
myself had so little notice. If others, with-
out being warned by me, have witnessed the
transit, I shall not envy their good fortune, but
rather rejoice, and congratulate them on their
diligence. Nor will I withhold my praise from
any who may hereafter confirm my observations
by their own, or correct them by anything more

k2

132

exact. Let us then briefly consider what assist-
ance may be expected from others.

In the space of half-an-hour, Venus advanced
towards the centre of the Sun a distance of 1' 24^' ;
of course, therefore, in twenty-six minutes she
had travelled to the extent of her o^vtl diameter,
namely 1' 12" ; that is, as much as, at the first
observation at fifteen minutes past three, the
antecedent limb of Venus had passed over the
Sun's limb; therefore forty-nine minutes past two
was the commencement of her eclipse.

At Uraniburg, where there was formerly an
observatory under Tycho, this would be forty-six
minutes past three, but the Sun set there at half-
past three, which is sixteen minutes before the com-
mencement of the ecli^Dse ; therefore nothing could
have been observed, even should astronomy not
have perished with its patron, and some should
be yet remaining who, having leisure for the
pursuit, sustain the ancient credit of Uraniburg.

At Goesa, in Zealand, where Lansberg lately
flourished, it commenced at fourteen minutes
past three, and the Sun set at fifty -five minutes
past three, consequently it might have been seen

133

there. But no one excepting Lansberg and his
friend Hortensius, both of whom I hear are dead,
would trouble themselves about the matter ; nor
is it probable that, if living, they would be willing
to acknowledge a phenomenon which would
convict their much-vaunted tables of gross in-
accuracy.

At Hesse Cassel the eclipse began at thirty-three
minutes past three, the Sun set at fifty-five
minutes past three. Providentially, Mr. Mogling
would be prepared for the conjunction with his
telescope, or at least with a tube furnished with
a narrower aperture than that which was formerly
used in observing Mercury ; if indeed there is
sufficient leisure in Germany to attend to subjects
of so trivial a nature to the neglect of more im-
portant afiairs.

At Paris, where Gassendi observed the con-
junction of Mercury with the Sun, the transit
was to be seen a little later than with us ; for the
first entry of Venus upon the Sun's disc took
place at six minutes past three, whilst the true
time of sunset was eight minutes past four, and
the apparent at twelve minutes past four, therefore

134

Venus was visible in the Sun for more than an
hour. Hence we shall consider Gassendi very
fortunate if he have found her no less accessible
than Mercury; and that neither unfavorable
weather nor inadvertence, of which it would be
wrong to accuse so celebrated an astronomer, de-
prived him of the opportunity.

In short, Venus was visible in the Sun
throughout nearly the whole of Italy, France,
and Spain ; but in none of those countries during
the entire continuance of the transit.

But America !

0 fortunatos nimium bona si sua norint !

Venus ! what riches dost thou squander on un-
worthy regions which attempt to repay such
favors with gold, the paltry product of their
mines. Let these barbarians keep their precious
metals to themselves, the incentives to evil which
we are content to do without. These rude people
would indeed ask from us too much should they
deprive us of those celestial riches, the use of
which they are not able to comprehend. But let
us cease this complaint, 0 Venus ! and attend to
thee ere thou dost depart.

135

** Wliy beauteous Queen desert tliy votaries here ?

All ! why from Europe hide that face divine,

Most meet to be admired ? on distant climes

Why scatter riches ? or such splendid sights

Why waste on those who cannot prize their value ?

Where dost thou madly hasten ? Oh ! return :

Such barbarous lands can never duly hail

The purer brightness of thy virgin light.

Or rather here remain : secure from harm,

Thy bed we'll strew with all the fairest flowers ;

Refresh thy frame, by labors seldom tried.

Too much oppressed ; and let that gentle form

Eecline in safety on the friendly couch.

But ah ! thou fliest ! And torn from civil life,

The savage grasp of wild untutored man

Holds thee imprisoned in its rude embrace.

Thou fliest, and we shall never see thee more.

While heaven unpitying scarcely would permit

The rich enjoyment of thy parting smile.

Oh ! then farewell thou beauteous Queen ! thy sway

May soften nations yet untamed, whose breasts

Bereft of native fury then shall learn

The milder virtues. We with anxious mind

Follow thy latest footsteps here, and far

As thought can carry us ; my labors now

Bedeck the monument for future times

Which thou at parting left us. Thy return

Posterity shall witness ; years must roll

Away, but then at length the splendid sight

Again shall greet our distant children's eyes."

136

CHAPTER lY.

It is proved that the spot observed in the Sun's disc was
really Venus.

The most skilful astronomers in their observation
of Mercury have been frequently deceived ; firstly,
those, who in the.time of Charlemagne, on the 16th
of April in the year 807, believed that the transit of
Mercuryover the Sun continued eight days: second-
ly, Averrhoes, who says in the Ptolemaic Par a;phrase^
that he recollected to have seen something of a
darkish appearance, and subsequently found by the
numbers that the conjunction of Mercury and the
Sun had been predicted ; he flourished about the
year 1160 of the christian era: thirdly, Kepler
himself, the most learned astronomer that ever
lived, was greatly deceived on the 18 th of May
1607. All these having seen spots on the Sun's
disc, an appearance not understood in those days,
rashly concluded them to be the planet Mercury;
but they were evidently misled, as circumstances
afterwards proved.

137

Are we then similarly deceived, and do we
mistake an ordinary spot for Venus ?

Verily since this may be doubted, as well by
some who are unacquainted with the heavens
except from books, as by others who are learned
and practical astronomers; and lest our labor
should be in vain, it may be worth while, before
further prosecuting the enquiry, to prove in a
satisfactory manner that the planet Venus was the
actual cause of this appearance.

Firstly, perchance there may be some who
believe that neither Venus nor Mercury could
ever be seen in the Sun, although they might be
upon his disc ; such, for instance, as suppose that
all the heavenly bodies shine with their own light,
and are neither opaque nor cast a shadow like
the Earth and Moon.

Secondly, others who, trusting to the astro-
nomical tables which they imagine as accurate as
their authors describe them to be, easily give way
to the same opinion, and deny that any real transit
took place on either the hour or the day we have
specified ; nor will they allow themselves to be
persuaded that tables, boasting so confidently of

138

their own accuracy, could possibly err to the
extent of a whole day, or miscalculate the situation
of Venus by several degrees.

But, thirdly, they will be the most astonished who,
having contemplated this beautiful planet, which
on a clear evening they think may even vie with
the Moon, shall learn from us her surprising
minuteness; and when they are told that the
common opinion of astronomers makes the
diameter of Venus equal to two-fifths of that of
the Sun, that is, ten times greater than we have
actually found it, they may possibly conclude that
we have been deceived by an ordinary spot, and
blinded by the desire of dignifying it with the
name of Venus.

Let others fear such a conclusion : for myself,
what I saw with my own eyes in the heavens,
suppHed me with sufiicient evidence of the
certainty of the observation, almost all the
circumstances of which I had predicted to my
friends; and I silently congratulate myself that
my correction of the motion of Venus, which I
had not before sufficiently appreciated, has been
confirmed beyond my utmost hopes. In order to

139

satisfy the doubts of others I make the following
remarks : —

Firstly, there is no occasion for any one to be
misled because Venus was deprived of that native
light which many erroneously attribute to the
planets ; for, by satisfactory arguments to be found
elsewhere, it is quite clear that the bodies of those
planets are obscure and derive their light exclu-
sively from the Sun.

Secondly, I should be more ready to commend
those who employ their skill in computing
Ephemerides, if, instead of servilely receiving the
report of others, they would trust something to
their own eyes. Indeed no one who has eyes and
who diligently avails himself of his opportunities
can be said to be so destitute of astronomical instru-
ments that he cannot observe many things in the
heavens, the knowledge of which, acquired with
so little trouble, would conduce greatly to the
advancement of the science. And although even
the best of the common tables may err, this
observation alone clearly shews that there are no
others which can supply their defects ; nor will
these tables even impugn its accuracy, as they
are less at variance with it than with each other.

140

Thirdly, they who are so astonished at the
minuteness of the diameter of Venus should rather
be surprised at those astronomers whose carelessly-
formed opinions have assigned such monstrous
proportions to the planets; for I will prove
that the diameter of Venus ought not to seem
greater than we in reality have found it.
But however much less it may be than the di-
mension usually attributed to it by astronomers,
it has nevertheless far exceeded the size of any
spot which I have observed. Schickard indeed
remarks, that " the solar spots sometimes appear
so large that they are visible through an opening
in a darkened apartment ; and that, from a small
aperture in a wine cellar, on the 6th of July,
1629, he had observed such an one which was
broader and darker than any that had come under
his notice, having a peduncle in the shape of a
pear." But these spots are rarely seen so large,
indeed I have never yet witnessed any to be com-
pared with this shadow of Venus, the common
ones scarcely equalling half-a-minute, except when
many are seen together so as to increase their
bulk.

141

But even if this spot of ours agreed with the
common ones in magnitude, yet we can shew,
by other and more certain, proofs, how it may be
distinguished from them. I have noticed particu-
larly three remarkable points of dissimilarity, of
which the first two are probable distinctions, and
the third a certain one.

First, as to figure. The figure of this body
was a perfect sphere, such as is usually attributed
to the planets, to the eternal bodies of the
universe, and to Venus herself. But the common
spots, which are nothing more than smoky exhala-
tions, or, as one may say, solar nebulosities,
consisting of fluid matter easily dispersed, are
rarely found to assume a spherical form, but are
of an irregular shapeless figure, and may be aptly
compared with the terrestrial clouds. Moreover
those spots which when seen upon the centre of
the Sun appear large and spacious, when upon his
limb or near the edge are compressed into a
lengthened figure, and are exceedingly subtile.
This proves that they do not possess a spherical
or globose shape, but one extenuated and difiusely
spread, and therefore that they are not stars as

142

some imagine. Ours then is no common spot,
since it retains unchanged the same spherical
figure and magnitude as exactly when in the
circumference of the Sun as when far distant
from it.

Second, as to color. Since the ordinary spots, or
solar nebulosities, are of rarer and less dense matter,
scarcely darker than that of thick smoke, they can-
not be said entirely to exclude the light of the
Sun, but rather to transmit its rays more faintly;
they are therefore seldom, if ever, perfectly black,
but are more frequently a darkish kind of color
mixed with light, especially round their edges
which no doubt are more rare than the centre.
But this beautiful shadow of Venus clearly
shewed that it proceeded from an opaque and
very dense body resembling the planets; for even
the Moon in a solar eclipse does not cast a
shadow denser, in proportion to its magnitude,
than the one which I have observed from this
spot.

Thirdly, and lastly. I found a remarkable
difference between the motion of this shadow and
that of the common spots upon the sun ; so that,

143

if other arguments were insufficient, this fact of
itself proves most clearly and incontestably that
it was a very unusual one, and occasioned by
Venus alone. Moreover, the common spots are
close to the surface of the sun and are carried
round with him, performing a revolution in the
space of a month, providing any of them happen
to last so lono\ Wherefore at the beo^innino^ and
end of their appearance, while passing round the
receding edge of the Sun, they seem to move at
so slow a rate that a day or two scarcely changes
their position, their approach to or departure from
our sight being as it were, in a right line. But that
which we observed, passed with a rapid and
uniform motion over the edge of the Sun,
traversing the twentieth part of his diameter in
half-an-hour, which the common spots have never
done in two whole days.

Perhaps I have argued this point at greater length
than it really merits ; not because I thought that
an astronomer would entertain a doubt as to
these spots which are visible almost daily upon
the Sun's disc, but that I might have an oppor-
tunity of explaining their nature and peculiarities.

144

For I know that there are some who make it
their business to deny with the most obstinate
and reckless malevolence the truth of our dis-
coveries, and who contend that these solar spots
are not temporary and fleeting vapours, but real
planets and durable bodies ; lest forsooth the
dogma of the Peripatetics, respecting the incor-
ruptibility of the heavens, should be impugned,
which our doctrine beyond all question effectually
opposes. Indeed the common spots are so different
in their nature from the stars that, even in the
centre of the Sun, they are frequently observed
to be engendered, to increase, to diminish and to
die away ; of which any candid enquirer may
easily convince himself But it is in vain to speak
of these things to those who will not hear, and
w^ho prefer their Aristotle, or to speak more plainly,
their own unreasonable prejudices to the clearest
demonstration. It is much easier to teach the
ignorant than those who will not learn.

Let such men make the most of their wdlful
blindness, and delight in their fables ; let them
keep to their worthy instructor, under whose
mantle they may safely retire ! I envy not their

145

ignoble dreams. At least, when astronomers
meet with an observation similar to ours, let
them know how to distinguish Mercury or Venus
from the common spots upon the Sun.

CHAPTER y.

An Examination of the apparent Longitude and Latitude
of Venus from the Sun.

A PLAIN statement of the observation having
now been made, and the truth of it proved, it
remains for us to explain of what advantage it
may be to astronomy. In the first place, the
apparent longitude and latitude of Venus from
the Sun's centre are to be computed ; and, with
this view, we annex an estimate of the distance
of their centres, and of the inclination.

But before proceeding, let us ascertain the
Sun's apparent diameter; for this will be our

L

146

surest guide in computing the distance between
tlieir centres. On this point astronomers differ
considerably : it was according to

Kepler 31' 1-

Tycho and Longomontanus 31' 54"
Lansberg 35' 50"

a very important difference, certainly, and one
not easily reconcileable with the laws of astrono-
mical science. For the present, however, I will
not advert to these inaccuracies ; but leave them
for fuller consideration at a future time, and
proceed to other matters. Let us then assume
the diameter of the Sun to be 31' 30", which is
nearly the mean of Kepler and Tycho, an estimate
which I adopt, not from regard to the idle adage
" medio tutissimus ibis," but because I have found
it, from my own repeated observations, to be very
close to the truth.

My circle having only thirty divisions, the
distances before given will have to be reduced
into minutes and seconds, of which the Sun's
diameter will be 31' 30", as the following table
will satisfactorily explain :

Fiij./.

E O

Jf-icf.:i,

=_1V

147

By the Clock.

The Distances of the Centres.

3.15

15' 17'

3.35

14' 10"

3.45

13' 39"

From these distances, together with a constant
inclination of 62° 30', the longitude and latitude
of Venus from the centre of the Sun was demon-
strated, as is shewn in the foregoing figure No. 2
in the plate, representing her true situation on
his disc, at her first entrance.

Let C be the Sun's centre, V Venus, E C L
the Ecliptic, ZCN the Vertical, Z the Zenith,
N the Nadir, C V the Distance of the Centres,
D C the Difierence of Longitude, D V the
Difference of Latitude; the angle VCN the
Inclination, N C L the Parallactic Angle or the
Inclination of the Ecliptic to the Vertical, E C V
the Inclination of the circle through the centres
to the Ecliptic.

The Parallactic Angle N C L is computed by
the doctrine of spheres ; the altitude of Culmina-
tion and the Sun's distance from it, together with
the Meridian Angle, being given by a well-known
method. To this is added the observed Inclina-

l2

148

tion V C N ; and thus it forms the angle VOL
whose complement to a semi-circle is the inclina-
tion of a circle through the centres to the Ecliptic
E C V. This being given, it will be as the radius
is to the distance of the centres C V, so the line
of the angle E C V is to the difference of the
latitude D V : and so the sine of the complement
is to the difference of the longitude D C. All of
which, in the three observations, are carefully
deduced in the following manner :

D.

M.

The true situation of the

sun .

12

24

The right ascension . .

*

250

55

The altitude of the Equator .

36

25

From these is given

D. M.

D.

11.

D. M.

The Hour

3 15

3

35

3 45

The Culminating degree . . .

27 34

2

23

4 48

The Meridian angle ....

78 37

76

54

76 4

The altitude of the Culmination

15 43

16

45

17 18

The distance of the Sun from )
the Culmination . . . . j

45 10

49

59

52 24

Therefore the angle IN" C L . .

70 56

68

53

67 55

To which V C ]Sr beicg added .

62 30

62

30

62 30

Gives the angle Y C L ...

133 26

131

23

130 25

To the complement of which E C V

46 34

48

37

49 35

M. S.

M. S.

m. s.

15 7

14 10

13 39

10 24

9 22

8 51

10 58

10 38

10 24

149

Answers
The distance from the centre Y C
The difference of longitude D C .
The difference of latitude D Y .

And thus are found the three distances of
Venus from the Sun, with respect to her longitude
and latitude.

In noting the observation, it is however obvious
that the Inclination is uncertain to one or two
degrees. Lest therefore it should be thought that
any great mistake with respect to the situation of
Venus might arise from this error, I will here
show how little is left in doubt. Imagine then
that I have erred 5°, and that the first hour of
observing is 3 15'.

The Inclination Y C IST

The angle Y C L wiU be ....
To the complement of which E C Y

Answers

The distance of the centres C Y . .

The difference of longitude DC. .

The difference of latitude D Y . .

The error therefore wiU be

In longitude

In latitude

D.

M.

67

30

138

26

41

34

M.

s.

15

4

11

19

10

2

0

55

0

56

150

It is clear therefore that an error of 5° in the
Inclination would not alter Venus' situation,
either in its longitude or latitude one minute,
which is very little. But I believe that I have not
erred 5°; therefore, the apparent situation of
Venus being satisfactorily ascertained, I shall
proceed.

CHAPTEE YI.

The alteration of the apparent into the true situation
of

I BEHELD Venus, during the transit, not from the
centre but from the surface of the earth ; there-
fore I observed her apparent and not her true
situation. Her true situation, which chiefly
concerns us, is only to be obtained by the
correction of the parallaxes, into which subject
I now proceed to enquire.

The hypotheses of all astronomers make the
parallax of Venus in so near an approach to the
earth sufficiently apparent ; but this I shall leave

151

to be further considered in a separate treatise,
and in the meantime retain my own opinion.

After much and repeated consideration, I find
the mean distance of the Sun to be equal at least to
15,000 semi-diameters of the earth. This para-
dox, as it may seem, diifers greatly from the
commonly received opinion ; nevertheless I trust
elsewhere to substantiate its correctness. Let us
now ascertain, from this distance of the Sun, the
distance and parallax of Venus.

According to observation, it was as the follow-
ing calculation shews, chap. 14 : —

The distance between the Sun and the Earth . 98409
The distance between the Sun and Yenus . . 72000
Therefore the distance between the Earth and

Venus 26409

Of which the mean distance of the Sun . . . 100000
But of semi-diameters this observation supposes 15000
And the distance of the Earth from Venus . . 3962
Venus therefore was distant from us just so many semi-
diameters of the Earth ; to which distance belongs —

M. s.

The horizontal parallax of Venus 0 52

From which the parallax of the Sun being sub-
tracted 0 14

Gives the parallax of Venus from the Sun ..038

152

Indeed so small a parallax will effect only a
trifling alteration ; and, if we were to take no
notice of it, the inconvenience would not be much
felt ; but since we have leisure let us remove even
these slight objections from our scrupulous oppo-
nents. It is not more trouble to apply the
parallax than to investigate it.

It is a problem sufficiently well known that the
parallax of the altitude of Venus, which differs
nothing from the horizontal on account of the
inconsiderable altitude of the Sun, is extended in
length and breadth; given therefore the paral-
lactic angle which I before computed in each of
the observations, and the following parallaxes are
obtained : —

The Hour. Of the Longitude. Of the Latitude.

3 . 15 0' 13'' 0' 36'-

3.35 0' 14'' 0' 35"

3.45 0' 14" O 35"

Venus was with the Sun in the western quarter
of the Zodiac, in longitude more east than the
centre of the Sun, in latitude more south, there-
fore the parallax diminishes the apparent longitude
from the Sun and increases the latitude ; hence,

153

in order that both may be true, we must add in
the one case and subtract in the other, which
being done, the true difference is given.

The Hour Of the Longitude. Of the Latitude.

3 . 15 10' 37" 10' 22-

3.35 9' 36'' 10' 3-

3.45 9' 5" 9' 49-

CHAPTER VII.

An Inquiry into the Time and Place of the True Con-
junction of Venus and the Sun.

I WAS not able to observe Venus at the actual
point of her conjunction with the centre of the
Sun, for both had set before she arrived there.
But as the chief utility of the observation depends
upon a knowledge of the true conjunction, I will
therefore represent it from those facts which I
was fortunate enough to observe.
The diurnal motion according to the calculation :

The direct motion of the Sun

The retrograde motion of Yenus ....
Therefore that of Yenus from the Sun was

D.

M.

s.

1

1

2

36

38

1

37

40

154

The differences of longitude which we have
found are next to be divided by this diurnal
motion of Venus from the Sun, that the time may-
be obtained which is to be added to the moment
of the observation, in order to give the true hour
of the conjunction, in this manner :

M. S. M. S. M. S.

The difference of longitude ... 10 37 9 36 95

Gives the hours 2 36^ 2 21^ 2 14

Add the hour of observation . . 3 15 3 35 3 45

Whichmakesthehour of conjunction 5 51^ 5 56^ 5 59

The moment of the conjunction, which from all
the observations ought to be exactly the same,
shews a difference of 7^, a small variation which
the impartial reader will easily excuse. The
medium between the extremes may be retained
with safety, and thus ascertained will be 5 55\

To obtain the true longitude at this moment,
the Sun's situation is to be computed, the situation
of Venus being apparently the same, but in
reality the contrary. Therefore from my calcu-
lation—

D. M. S.

The true situation of the Sun is . . . . 12 29 35
And that of Venus wiU be 12 29 35

155

So far for the longitude. But as the situation of
Venus is at length clearly known, and the latitude
is made evident, it is necessary to ascertain it also
at the hour of conjunction.

The diurnal variation of the latitude of Venus
is assumed from calculation to be 15' 40" ; and
because the latitude was south around the north-
ern node, it therefore decreased, as this observation
likewise shews. The diurnal variation of the
latitude must therefore be divided into the hours
and minutes in which the true conjunction
followed the observation, and the quotient added
to the observed latitude in this manner :

r. M.

In hours 2 40

The latitude decreases ... 1 44

The observed latitude . . .10 22
Therefore at the hour of con-

junction 8 38 8 32 8 24

The first observation differs from the third 0' 14",
which is of no importance ; but if, as before,
we take the mean, the latitude will be ascertained
at the hour of conjunction to be 8' 31'' south.

D.

M.

D.

M.

2

20

2

10

1

31

1

25

10

3

9

49

156

CHAPTER YIII.
The Demonstration of the Node of Venus.

It will conduce much to the improvement of
astronomy if the node of Venus be shewn ; there-
fore to demonstrate this from what is already
discovered, let S in the foregoing figure No. 1 in
the plate represent the Sun ; T the Earth ; V
Venus ; E N the portion of the Ecliptic ; 0 V N
part of the orbit of Venus ; N the Northern Node ;
E N V the inclination of the orbit of Venus to
the Ecliptic, which on the authority of Kepler I
assume to be 3° 22'; E T V the apparent angle
of the latitude of Venus on the Earth 8' 31" from
observation ; S E the distance between the Sun
and Venus ; T E the distance between the Earth
and Venus. From these the distance of the node
E N from the place of the conjunction is thus
computed :

1st. In the plane triangle T E V
The right angle T E V is given n. m. s.

"With the angleETY 0 8 31

And with the side T E 26409

157

D.

M.

s.

Therefore the side E Y

0

0

65

2nd. In the plane S E Y

The right angle S E Y is given

And the side SE

72000

With the side E Y

0

0

65

Therefore the angle E S Y (or the arc E Y)

0

3

7

3rd. In the spherical triangle I^ E Y

The right angle at E is given

The arc EY...

0

3

7

And the angle E :N" Y

3

22

0

Therefore the arc KE

0

53

10

Let the place of the conjunction be added to this

n

12

29

35

Which makes the longitude of the node

n

13

22

45

But the node of Yenus is according to

Kepler

n

13

31

13

Longomontanus

n

14

32

6

Lansberg ...

n

11

56

4

I cannot pass over, without astonishment, this
difference of opinion, so much to be regretted
among astronomers of such celebrity ; nor is the
result unimportant, so great is the discrepancy,
for it changes the latitude of Venus in this
position nearly half a degree ; and although
elsewhere in more remote distances, the variation
may not be so perceptible, yet it never disappears

158

so completely as not to be a great reflection upon
our astronomers who err to such an extent ; and
the more so as from other observations now-
extant, they might so much better agree among
themselves. Lansberg, who aggravates his fault
by foolish boasting, is one of those chiefly to
blame ; nor is Longomontanus, who possessed to
so little purpose the observations of his friend
Tycho, much more excusable; but here as
elsewhere, the ingenious Kepler errs least of all.

CHAPTER IX.
The beginning, middle, and end of the Transit are shewn.

We have already spoken of the hour of the true
conjunction in respect of the ecliptic, but as that
was not the middle of the transit, nor was there
shewn in it the nearest distance of the centres, it
may perhaps be agreeable to some, though it is
not otherwise of much use, to assign the true

159

middle, together with the beginning and end,
of so unusual and wonderful a conjunction.
For this purpose, let a figure be drawn, such as
No. 3 in the preceding plate, and let C be the
Sun's centre ; N the Northern node ; E C N the
ecliptic ; I N the orbit of Venus ; I the beginning
of the transit ; M the middle ; F the end ; V the
true conjunction in respect to the ecliptic ; C V
the latitude of Venus at its true conjunction ; C
M the least distance of the centres in the middle
of the transit ; C N the distance of the node from
the place of the true conjunction ; E N I the
visible inclination of the orbit of Venus to the
ecliptic. From these the periods of incidence
M I and IMF are thus computed :

1st. — In the triangle Y C N the right angle
Y C ^N" is given.

The side C IS" (chap. 8)

The side C Y (chap. 7)

Therefore the angle C E" Y

And to this Y C M is equal, whence moreover
the right angle Y M C is given with the
sideCY

Therefore the side Y M

And the side CM

D.

M.

s.

0

53

10

0

8

31

9

6

0

0

8

31

0

1

21

0

8

24

160

D. M. S.

1

37

40

9

6

0

1

38

55

0

1

21

0

19

30

5

55

0

6

14

30

2nd. — The diurnal motion of Yenus from the
Sun which I before used is less than in her pro-
per orbit. To find this in the triangle Y C ^.
Let the right angle Y C N be given.

The diurnal motion in the Ecliptic C K

With the angle C K Y

Therefore the diurnal motion in her orbit Y !N"

Ey this let Y M be divided

The horary periods are

Which must be added to the moment of the true
conjunction

That the middle of the eclipse may be found ...

3rd. — For the periods of incidence in the triangle
IMC the right angle at M is given.

With the side C M 0 8 24

And the sum of the semi-diameters of the Sun
and Yenus C I

Therefore the periods of incidence I M

Divided into the diurnal motion

Give the time of incidence .,.

In a similar manner they are computed by the
difference of the semi-diameters as in a total
eclipse of the Moon.

The periods of half the eclipse . . .

The time of half the eclipse

Therefore the first ingress will be

The total ingress

The middle

The first egress

The total egress

0

16

23

0

14

4

1

38

55

3

25

0

0

12

34

3

3

0

Hour

2

49

30

3

11

30

6

14

30

9

17

30

9

39

30

161

CHAPTER X.

An Examination of the Cahulations of Astronomers
respecting the foregoing.

The value of this observation, in correcting the
motion of Venus, has already been explained.
We must next ascertain how the facts which are
deduced from it agree with the calculations of
astronomers. This inquiry will doubtless shew
the usefulness of the observation to the practical
student ; especially as it will appear that even the
best astronomers have not only disagreed among
themselves, but have considerably deviated from
the truth.

There are four astronomers from whose tables
Ephemerides are at this time chiefly computed,
into whose respective merits, as there is some
difference of opinion, it may be well carefully to
inquire.

1st. Copernicus who compiled the new, or
rather the renewed, hypotheses, and the laws of
the sidereal motions, in six books of Revolutions,

M

1G2

from which Erasmus Reinhold afterwards con-
structed the Prutenic tables ; and fi-om these,
Origanus, Maginus, and others derived their
Ephemerides which are still extant, and are
chiefly used in our prognostics, though now the
Prutenic calculation is held in less esteem.

2nd. Longomontanus, the disciple of Tycho
Brahe, and as it were the heir of his discoveries,
who, in his Danish astronomy, treading faithfully
in the footsteps of his master, brought to a con-
clusion those things which Tycho was by death
prevented from finishing.

3rd. The sagacious Kepler, who formerly
assisted Tycho in his calculations, was afterwards
astronomer to three Emperors, and happily
effected the renovation of the science by the
publication of the Rudolphian tables, to which
his other writings may be considered a prelude.

4th. Lastly, Lansberg, who undervalued the
labors of his predecessors, and with much assur-
ance endeavoured to substitute his own perpetual
tables of the celestial motions, loading them to
satiety with the praises of himself and others.

I will give the calculations of these four men,

163

in order that it may appear who has best explained
the difficulties respecting Venus, and who, in
other respects, is most safely to be trusted. This
observation is well suited to the purpose ; for the
calculation may answer tolerably well in very
great distances from the Sun, though it is other-
wise erroneous: greater accuracy is necessary in the
inferior conjunction; and unless the calculation be,
as it were, held together, it will betray gaping
chinks, and the smallest error will be detected. It
also happens, though why I do not know, that what-
ever is faulty in the hypotheses of the astronomers
shews itself principally here, the errors being in
this instance accumulated, and not compensating
one another as is sometimes the case.

But I shall be content to set forth the calcula-
tion from their tables alone, and will not weary
myself nor my readers with any geometrical
delineation of hypotheses or superfluous compu-
tations of triangles ; for there is no need of such
nicety in refuting gross errors, neither is it
necessary to waste paper in a prolix display of
circles or in a description of hypotheses, which are
incorrect in their very form.

M 2

164

Come then, ye renowned astronomers of our
o^vn times ! Behold here a noble reward, — Venus
promises Urania, fairer than any Helen, to him
who shall happily win her.

CHAPTER XI.

The Calculations of Copernicus.

I shall commence with the incomparable Co-
pernicus, the successful reviver of what Gellibrand
calls the " noble hypothesis of the motion of the
Earth," whom all the lovers of astronomy have
hitherto followed, and will doubtless continue to
do. Having long contemplated and admired a
philosophy so sublime and so worthy of a Chris-
tian, I thus expressed my aversion to the puerile
fictions of the pagan Ptolemy : —

Why should' st thou try, 0 Ptolemy, to pass
Thy narrow-bounded world for aught divine ?
Why should thy poor machine presume to claim
A noble maker ? Can a narrow space

165

Call for eternal hands ? Will thy mansion
Suit great Jove ? or can lie from such a seat
Prepare his lightnings for the trembling earth ?
Fair are the gods you frame forsooth ! nor vain
Would be their fears if giant hands assailed them.

Such little world were well the infant sport
Of Jove in darker times ; such toys in truth
His cradle might befit, nor would the work
In after years have e'er been perfected,
When harlot smiles restrained his riper powers.
These are your fancied gods, your paltry dreams ;
And worthy them is all you raise around ;
The temples that you bmld are amply large,
Thy heavens are suited to a Jove like thine.

Are such the auspices by which you rule
Your world ? No longer I deplore the earth
That stands begirt with soUd adamant ;
Such walls repel unholy deities,
And keep the nations pure. How wisely doth it
Court repose far from the stars where it would
Have to mingle in degrading commerce.
And find, not heaven, but realms replete with crime.

Calm urge thy chariot through the starry sphere,
0 Phoebus ! crowds oppressed with wine can bear
No tumult. Now the banquets of the gods
Are spread by one, a youth, whose limbs betray
His steps, whose head in whirling motions lost

166

Can never mix the cup with steady hand.
Yet spare thyself, thy labor wisely cease,
And while the sober deities recover
Their sounder senses, let thy jaded steeds
Renew their strength with nectar and ambrosia.
ISo trifling task it is to hurl at once
So many gods and stars in uniform
Gryration. Then let those whose little sum
Of learning reaches but to tell the tale
Their fathers told before, whose every word
Deals in absurdities unworthy heaven,
Rival each other to applaud this fable.

But a sublimer throne is thine, and awe
Ineifable awaits thy lightning's course,
Thou God of truth whose certain laws direct
The starry spheres, whilst all the powers above
Admire and tremble ; the projected Earth
Rolling along its planetary path
Hath learned to hail thy triumph ; and this age
Enables mortal eyes in thy great works
To view thee nearer, and with nobler thought
To trace the stars whose order proves them thine.
In vain the Sun his fiery steeds would urge.
In vain restrain them, or attempt to guide
Their rapid course within the laws of fate.
The Earth performs their task, and by each day's
Revolving saves to all the distant stars

167

The useless labor of unceasing motion.

The clouds which once obscured our mental sight

Are gone for ever ; great Copernicus,

Sent from above, lays open to our view

The arduous secrets of wide heaven's domain.

Turn hither then your grateful steps, for here

Are wondrous mysteries that you may learn.

Open to all whom, freed from baser thoughts,

The love of truth impels, and whom no cry

Of vulgar men can scare from what is right,

Nor fear oppress, 0 child of ignorance !

'Nor fabling oracles once deemed divine.

It was sufficient for Copernicus to have laid so
good a foundation, we must pardon him if, his
sublime understanding being perplexed by some
few inaccurate and fallacious observations, he
failed in rearing the superstructure ; for he neither
discovered the true form of motion, nor did he
ascertain the numbers with precision, being too
much devoted to the circles and equality of the
ancients, as appears from this observation which I
thus calculate from his tables, assuming the
difference between the meridian of Frueburg and
our own to be 1° 30'.

168

Of the Suk".

SEX. DEG. MIN, SEC.

Simple equable motion (sequalis simplex) .3 44 14 29

The simple anomaly of the Equinoxes . ,2 58 40 46

The prosthaphceresis of the centre to be added 0 10 53
The proportional parts (scrupula propor-

tionalia) 0 0

The mean anomaly of the Sun 2 31 53 16

The coequate anomaly (anomalia coequata) . 2 32 4 9
The prosthaphceresis of the orbit to be sub-
tracted 0 53 12

Therefore the true simple motion of the Sun 3 43 21 17
Of Yenus

The apogee 0 48 20 0

The anomaly of the centre 2 55 54 29

The prosthaphceresis of the centre to be sub-
tracted 0 8 43

The proportional parts (scrupula propor-

tionalia) 59 53

The eccentric longitude 3 44 5 46

The mean anomaty of the orbit 2 58 48 7

The equate anomaly of the orbit , . . .2 58 56 50

The prosthaphceresis of the orbit to be added 2 50 20
Therefore the situation of Venus by the

fixed stars 3 46 56 6

The south latitude 0 21 30

In the latitude there is a small error, not indeed

more than 13'; but in the longitude there is a
very considerable one, for Venus, who was actually

169

in conjunction with the Sun, was distant from it,
according to this calculation, 3° 34' 49", and as
her diurnal motion from the Sun is 1° 3? 40",
they were in conjunction the day after, at four
minutes and forty-seven seconds past two.

Therefore it is not on account of Mercury alone
that Schickard may pity the vanity and unskil-
fulness of the astrologers who, putting forward
their tables as true, trifle with the fate of posterity.
Venus does not smile upon their absurdities :
what good luck is destined for me ? what sort of
a wife? the inconstant Mercury is propitious,
will not Venus, whom the astrologers conciliate
by such well- contrived calculations, be so likewise ?
I perceive that I must apply for other assistance
than the scheme of my nativity affords which, so
far from telling my fortune, does not even indi-
cate what is already revealed. Are the astrologers
then, who are so profoundly ignorant in certainties,
to be credited in doubtful matters ?

I have computed the situations of Venus and
the Sun from the fixed stars, because we are here
seeking their distances only ; but if you should
desire the longitude from the true equinox, add

170

to their situation, with reference to the fixed stars,
the true precession of the equinoxes 28° 27' 23",
and you will obtain it.

CHAPTEE XII.

The Calculation of Lansherg.
Lansberg, a true disciple of Copernicus, follows
him very closely; indeed his numbers only differ
slightly respecting some of the planets ; but his
formula of the hypotheses scarcely varies from
that of his master. His astronomy is therefore
nothing more than a second edition of the Pru-
tenic tables. In some things perhaps he is a
little more elaborate ; but, in most, certainly
more faulty than his original. Nevertheless he
earnestly recommends his immortal fame to pos-
terity; and, under a pompous title, offers his tables
as compiled from and agreeing with all sorts of
observations, without fear of detection. Let him
not be angry if we should prefer, rather than
himself, those whom he so superciliously con-
demns : and that it may be known with what
justice he so confidently boasts of his own labors.

171

let him explain, in his own words, that most
accurate calculation which he has made the
subject of so many encomiums.

From the commencement of the Christian era
to the time of this observation there are 1638 full
Julian years, 10 months, 23 days, 5 hours, and
55 minutes, under the meridian of Liverpool;
under that of Goesa 6 hours and 20 minutes ap-
parent time, or when properly corrected 6 hours and
4 minutes, this is, in Sexagence dierum, 2"' 46" 16',
46 days, 15' 10",* by which the following motions
are given.

Or THE EaUINOXES. SEX. DEG. MIN, SEC-

The anomaly 5 58 32 51

The prosthaphseresis to be added .... 12 30

Of the Sun.

The mean motion (motus medius) . . . .4 13 3 38

* As the general reader may not understand this mode of calculation,
it may be well to state that Horrox takes it from Lansberg who
adopts, for the arrangement of his tables, what he called SexagencB
dierum. According to his method, 60 days make a sexagena jprima,
60 times 60 or 3600 days a sexagena secunda, and s > on. Hence, in
conformity with a calculation which he gives, we have

3a 2a la Dies

1600 Julian years 2

42

20

0

38 do. do

3

51

19

The ten first months of a common year

(1639 was not bissextile), or 3_o_4 . .

5

4

Additional days in November ....

23

46 16 46 of

time calculated in sexagence ascending; together with lo' 10" of
scrupula descending.

172

SEX. DEG. MIX. SEC.

The anomaly of the centre 3 164S 7

The prosthaphseresis of the centre to be added 1 42 50
The proportional parts (scrupula propor-

tionalia) 1 20

The mean motion of the apogee .... 1 35 54 49

The equate motion of the apogee . . . .1 37 37 39

The true anomaly of the orbit 2 35 25 59

The prosthaphseresis of the orbit to be sub-
tracted 0 51 47

The mean motion of the Sun from the true

Equinox 4 13 16 8

Therefore the Sun was in 4 12 24 21

Op Yentis.

The mean motion of the apogee . . . .1 31 47 11

The anomaly of the centre 2 41 16 27

The prosthaphaeresis of the centre to be sub-
tracted 0 39 9

The proportional parts (scrupula propor-

tionalia) 58 12

The longitude of the centre 4 12 24 29

The mean anomaly of the orbit 2 59 50 31

The equate anomaly of the orbit .... 3 0 29 40
The prosthaphaeresis of the orbit to be sub-
tracted 1 19 52

Therefore the longitude of Yenus from the

mean Equinox 4 11 4 37

Erom the true Equinox :^ 11 17 7

The mean motion of the northern node . .1 11 43 34

The distance ofYenus from the northern node 3 0 40 55

Therefore the north latitude ofYenus . , 0 10 45

173

The observation shews Venus in conjunction with
the Sun ; this calculation separates them 1° 7' 14".

Therefore the conjunction by computation was
earlier by 16 hours 31 minutes.

The observation decreases the latitude south,
while the calculation increases it as much north.
Hence the studious may perceive how little these
perpetual tables, which their author so loudly
praises, are to be relied upon ; certainly a little
more modesty would have been more consistent
with their pretentions than so many undeserved
compliments, which among prudent people have
the effect of lessening rather than of increasing
confidence.

No one who is disposed to favor Lansberg must
be blamed ; the diameter and parallax are, in his
opinion, assumed to be different from these
statements. But, if we should follow him in the
longitude, both causes, and in the latitude the
former, would increase the error.

174

CHAPTEE XIII.

T]ie Calculation of Longomontanus.

It may perhaps be some consolation to the
admirers of theLansbergian astronomy, if there are
any, to learn that the followers of Tycho, disowned
by their master and to whom Hortensius, the
advocate of Lansberg, strenuously denies the
merit of having perfectly restored the science of
astronomy, (see Preface to Lansberg's Motion of
the Earth), labor under a similar or even a greater
error ; and, lest I should seem to envy them the
miserable satisfaction "habuisse socios," I will edify
their dull souls by convicting Longomontanus,
Tycho's disciple and his too faithful follower in all
things whether true or false, of a most palpable
blunder. His calculation is thus :

To the current year of our Lord 1639, 24th
day of November 5 hours bb minutes at Liverpool;
or 6 hours 52 minutes by apparent time, and 6
hours 46 minutes by mean time at Uraniburg
these motions are given.

175

Of the Equinoxes. sex. dbg.

The anomaly 3 20

The prosthaphseresis to be added ....

Of the Sun.

The equable motion (motus sequalis) . . .4 13

The apogee 1 36

The anomaly of the orbit 2 36

The prosthaphseresis of the orbit to be sub-
tracted 0

The mean motion from the true equinox . .4 13

Therefore the Sun's situation . . . . t 12
Of Ye^sUs.

The apogee 1 30

The anomaly of the eccentric 2 42

The prosthaphseresis of the ecccDtric to be

subtracted 0 33 5

The proportional parts (scrupula propor-

tionalia)

The eccentric longitude 4 12

The mean anomaly of the orbit 3 0

The equate anomaly of the orbit .... 3 0
The prosthaphaeresis of the orbit to be sub-
tracted 2 28 37

Therefore the longitude of Yenus from the

mean equinox 4 10

From the true equinox :^ 10

The mean motion of the northern node . .1 14

The distance of Yenus from the northern node 2 58

Therefore the south latitude 0

30

28

9

36

9

13

15

14

53

59

49

46

18

49

29

3

22

30

46

43

58

30

36

8

20

55

54

0

7

31

17

7

22

30

13

38

7

40

176

The latitude is sufficiently correct, but the longi-
tude errs 2° 11' 56", and hence it is one day, eight
hours, and twenty-five minutes too little. In the
latitude, therefore, he is more correct than Lans-
berg, but in the longitude he is almost twice as
much at fault ; nevertheless I do not wish it to
be thought, from this one instance, that Lansberg's
tables are superior to his in other matters, for I
have often proved that Longomontanus is more
correct as to the three superior planets, and also
with respect to the moon.

CHAPTER XIY.

The Calculation of Kepler.

But I leave these patrons of circles and equality,
these artificers of an useless labyrinth, and their
hypotheses which are faulty in their construction
and incapable of amendment. For although the
measures of the eccentricities of the orbits,
together with the mean motions, might be cor-

177

rected so as to resemble this and other observa-
tions ; yet as the stars are governed by different
laws from those which they have invented, it is
impossible by a complication of such circles to
bring about an entire agreement with appearances.
I hasten therefore to that prince of astronomers,
Kepler, to whose discoveries alone, all who under-
stand the science will allow that we owe more
than to those of any other person. I venerate
with the greatest honour and admiration his
sublime and enviably happy genius; and if
necessary, I would defend with my best efforts
the Uranian citadel of the noble hero who has
so much surpassed his fellows, nor shall any one
while I live, violate his ashes with impunity.
His death was an event that must ever have
happened too soon ; the science of astronomy
received the lamentable intelligence whilst left in
the hands of a few trifling professors who had
kept themselves concealed like owls until the
brightness of his sun had set.

Who, mighty shade, shall sing thy praises ? who,
Worthy so great a task, shall reach the stars ?

N

178

Who now shall chant thy fate ? The modern seers

Portend that heaven's disturbed by monsters which

Are unintelligible to mankind ;

Perchance in pity thou dost still protect

The weaker minds of those whom thy decease

Hath robbed of nature's best interpreter.

Since such a guide is lost, what other now.

Deserving to succeed, can take the reins ?

Or should the stars rebel, who can restore

Them to their course, and bind with closer ties

Their wandering ways ? 0 ! thou alone couldst take

The arduous guidance and shake the strong rein

To urge along the slothful retinue ;

By thee restrained, the vulgar crowd

Dared not to cHmb the sacred car of heaven.

No devious course could cause thy thoughts to wander

In perplexity ; fictitious circles

Could not enthrall thy loftier genius ;

But thy mind, intent on the subHme, with

Faithful hand traced the motions which the God

Of nature hath decreed. While yet the power

Was thine to guide their way, true to thy rules

Each planet in its ordered path revolved,

And all rejoiced to follow in thy train.

But now deprived of thee science declines.

Sinking in antiquated errors ; all

The stars are hurled as madness may devise,

179

And heaven's deformed by senseless violence !

Unliappy Grermany ! though torn by wars,

The sword alone will not effect thy ruin ;

A heavier curse conspires to brmg about

Thy mind's destruction. 'Tis this encourages

Hortensius to insult Pelides' dust ;

By this the pompous Belgian, bolder grown,

Imposes on the world Perpetual Tables,

And spurns the embers which a powerful flame

Has sadly left ; nor does he even fear

Lest his bold thefts should haply be detected,

[N'ow that great Kepler's numbered with the dead.

Chaos is come again, the world's unhinged,

All things, in thee o'erpowered by fate, betray

The noblest art to trifling sycophants.

Kepler's Rudolphian tables give the following
calculation of the observation, the time having
been before reduced and settled by Longomon-
tanus.

UF THE bTJN. sex. deg. min. sec.

The equable motion (motus aequalis) ... 4 13 18 7

The apogee 1 36 24 5

The mean anomaly 2 36 54 2

The equation to be subtracted 0 49 32

Therefore the Sun's situation . . . . f 12 28 35

The distance between the Earth and the Sun 98350

N 2

180

Of YeNTTS. sex. dec. mix. SEa

The equable motion 11319 2

The aphelion 5 2 4 57

The mean anomaly 21114 5

The equation to be subtracted . . , . . 2 10 36 4

Therefore the eccentric longitude . . . .1 12 42 58

Eeduced to the ecliptic ., 112 43 4

The distance between the Sun and Venus . 72084
The anomaly of the commutation .... 3 0 14 29
The prosthaphoeresis of the orbit to be sub-
tracted 0 39 43

Therefore the apparent situation of Yenus f 11 48 52

The northern node 1 13 31 13

The distance of Yenus from the northern node 5 59 11 45

Therefore the south latitude 0 7 45

In tlie longitude there is an error of 39' 43", which
is as much as the prosthaphoeresis of the orbit,
and gives 9 hours 46 minutes, by which quantity
the conjunction was earher.

In the latitude, the calculation is only slightly
defective. Hence it is clear that Kepler's tables
represent the situation of Venus in the Sun the
most correctly of all, and in this respect at least,
are to be preferred. I have also found them
better in various ways, both from my own obser-
vations and from those of others.

181

CHAPTEE XV.

Correction of the Motions according to Rudolphi,
Since the error which I discovered in the Rudol-
phian tables is so great, it may not be amiss to
shew how the calculation may be amended in
order to agree with this and other observations.
I quite agree in the form of Kepler's hypotheses,
and gladly receive both his annual and diurnal
motion of the earth. I am of opinion also that
these motions do not arise from complicated
fictions of useless circles, but from natural and
magnetic causes, and that they are owing to the
rotation of the Sun on its axis. He knows but
little of astronomy who is ignorant that the
figure of the orbit is elliptical ; that its centre is
the body of the Sun, and not a fictitious point
near it : that the motion of the planet is really
unequal ; that the whole apparent inequality does
not proceed from its eccentricity alone ; and
finally, that the inclination of all the orbits to the
ecliptic is not influenced by the annual motion,
but is fixed and constant. No one, we repeat,
who denies such facts is sufficiently acquainted

182

with astronomical observations. They are all
fully demonstrated by Kepler, and I have found
them, by subsequent examination, to be strictly
true ; but with the view of attaining greater
perfection in the theory constructed upon these
principles and in the quantity of the mean motions
and eccentricities of the orbits, I have attempted
to correct the motions of the Sun and Venus in
the following manner ; an undertaking which
could not be displeasing to Kepler himself, as he
frankly confessed that these matters were not yet
thoroughly explored.

I. OF THE SUN.

1. The mean motion of the Sun, as to its
periodical quantity, is correctly determined by
Kepler, but it seems to me that one minute should
be subtracted from its roots ; the places of the
fixed stars however ought not on that account to
be diminished, as Longomontanus has hastily
concluded.

2. The apogee is right in all respects.

3. The eccentricity which he makes 1800 with
a radius of 100,000, I make, for many reasons,
only 1735. Therefore the greatest equation will

183

be, according to me, 1° 59' 18'' ; whereas according
to him it is 2° 3' 46"; and herein lies Kepler's
principal error which has betrayed him into many
others, as I shall shew at another opportunity.

4. The last correction which I shall make
relates to the triple method of equalizing the
natural days in the astronomical or Emperic
demonstration of Tycho, and in the physical one
of Kepler. The correction of the lunar motion
requires this, and the diminished eccentricity of
the Sun explains the difficulty in which Kepler
was so deeply involved ; but more of this in its
proper place, God willing.

II. OF VENUS.

1. I find the mean motion of Venus much
slower than Kepler makes it, namely about 18' in
a hundred years; but in the beginning of the
present year, 1640, 9' 20" should be subtracted,
and hence arises the chief cause of the great
discrepancy in the calculation of Rudolphi con-
cerning this observation.

2. The aphelion, in this age, remains at 5°
in ^', and the observations of our predecessors
seem to allow it scarcely any, or at least, an ex-

184

ceedingly slow motion. Hence it is clear wliy
those who refer the eccentricities of the planets
to the centre of the great orbit of the Earth, find
the eccentricity of Venus less at this day than
what Ptolemy has recorded ; for he added, during
the advance of the apogee, the moveable centre
of the orbit of the Earth to the fixed centre of the
orbit of Venus.

3. The true eccentricity is 750, and the semi-
diameter of the eccentric of Venus 100,000 ;
therefore its greatest equation is 51' 34", whereas
according to Kepler, the former is 692, and the
latter 47' 36".

4. The radius of the orbit of Venus is to the
orbit of the Earth as 72,333, not 72,414 as he
fixed it, to 100,000.

5. It has already been demonstrated that
8' 30" are to be subtracted from the northern
node, from the beginning of the year 1640, which
may also be done hereafter in other ages.

6. The inclination of the orbit to the echptic
appears slightly to exceed the calculation of
Kepler. He has fixed it at 3° 22' whilst I make
it 3° 24' ; but certainly it is not so much as 3° 30',
as Lansberg and Longomontanus suppose.

185

I partly began these corrections of the Rudol-
phian tables before the transit of Venus, from
other observations ; and afterwards considerably-
amended them by further experiments very
carefully instituted. I have also brought this
calculation, otherwise tolerably exact, to coincide
even in the minutest particulars with our obser-
vation, in the following manner : —

Of the Sun. sex. deg. min. sec

The equable motion (motus sequalis) . . .4 13 17 22

The apogee 1 36 24 5

The mean anomaly 2 36 35 17

The equation to be subtracted 47 47

Therefore the situation of the Sun . . .f 12 29 35

The distance between the Sun and the Earth 98409

Of Yentjs.

The equable motion (motus sequalis) . . .1 13 10 16

The aphelion 5 5 0 0

The mean anomaly 2 8 10 16

The equation to be subtracted 40 47

Therefore the eccentric longitude .... 1 12 29 29

Eeduced to the ecliptic 1 12 29 35

The distance between the Sun and Yenus . 72000

The northern node 1 13 22 45

Distance of Yenus from the northern node . 5 59 6 44

Therefore the south latitude 8 31

186

You see here that, agreeably to our expectation,
Venus was exactly conjoined with the centre of
the Sun; therefore there is no anomaly of the
commutation, nor prosthaphoeresis of the orbit.
You also see that the latitude and other particu-
lars exactly agree with the observation ; this
result indeed might easily be obtained from a single
example, but it would be tedious, and foreign to
the subject in hand, to shew what might happen
in other circumstances. I ask therefore that
credit may be given to my bare word for the
present ; and, with God's permission, by further
collating and condensing my proofs, I will cause
Venus to arise from this sea of error, to come
forth, wrapt in the chain of numbers, more
beautifully than she did from the arms of Vulcan,
and to learn a modesty unprecedented in her
former deportment ; nor, as heretofore, shall she
wander in wanton lasciviousness, evading and
despising the care of her guardians whose councils
have been so little attended to, as we have already
plainly seen :

Tantae moHs erat muHebrem frangere mentem.

187

CHAPTER XYI.

On the diameter ^ Venus.

Congratulate us, Gassendi, on clearing from
suspicion your observation of Mercury, and let
astronomers cease to wonder at the surprising
smallness of the least of the planets, now they
find that the one which seemed the largest and
brightest scarcely exceeds it. Mercury may well
bear his loss since Venus sustains a greater.

I observed the diameter of Venus (Chap. I.)
to be 1' 12", the Sun being 30'; therefore the
latter being 31' 30", the true diameter of the
former is 1' 16". My friend Mr. Crabtree's obser-
vation agrees with this calculation : I am sure
she did not appear greater ; if there is any error,
it is in an excess. There is no reason why any
one should doubt the truth of the observation ;
unless indeed he is unacquainted with the
telescope, or influenced by the knavery of the
Peripatetics, or suspects our honesty ; and I shall
not stay to argue either with those who have not
seen this instrument or who mistrust its fidelity,

188

for it is vain to contend with ignorance and self-
will. Permit me to remind any who may suspect
our good faith, how easy it would be to investigate
the subject for themselves, and how little it would
serve our purpose to distort truth by falsehood.

Let us then examine the opinions of others, in
order that it may appear with what degree of
accuracy astronomers have hitherto estimated the
magnitudes of the stars.

1. Tycho Brahe, in whom most men place
confidence in such matters, makes the diameter
of Venus 3' 15" in her mean distance from the
Earth. But the distance of Venus from the
Earth according to our observation was 26,409,
and the mean distance of Venus or the Sun from
the Earth 100,000 as was before shewn ; therefore
Venus, who from the distance of 100,000 appears
to be 3' 15", at the distance of only 26,409 will
be 12' 18". But this is far from the truth, being
nearly ten times as much as in the observation.

2. Philip Lansberg, who boasts so authorita-
tively of his Uranometria, makes the diameter
of Venus in her mean distance 3' 0"; therefore
at the distance before-mentioned, it would be

189

11' 21^ This is very far from the mark, being
nine times greater than in truth it should be.

3. From the tables of Rudolphi, according to
the precepts of Kepler, the diameter of Venus, by
our observation, is computed to be 6' 51"; his is
the nearest approach to the truth, as is generally
the case with Kepler, but still it is five times or
more in excess.

Copernicus and Longomontanus say nothing
of the diameters of the five primary planets ; but
the ancients, Alphraganus and Albategnius, difl^er
very little from Tycho and Lansberg.

Since therefore the observed diameter of Venus
differed so considerably from what has been
assigned by the whole school of astronomy, it
may perchance be doubted whether some optical
deception has not caused it to appear small; for
Schickard, an excellent mathematician and pro-
fessor of Hebrew and astronomy in the university
of Tubingen, supposed that such was the case
with respect to the Mercury of Gassendi, the
minuteness of which caused equal astonishment.
The reasons why he supposed Mercury in the
Sun to be diminished below the truth, as they

190

apply equally to Venus, I shall briefly subjoin,
and with the author's permission, examine ; for
I observe that some sensible men acquiesce in
his opinion, and, from not having sufficiently
considered the subject, at once take for granted
that which connects, upon any grounds, new
appearances with old opinions.

1. He takes his first argument from the
diffusion of the solar light. "You know" says
he "it is the nature of this light to spread and
diffuse itself on all sides, hence it necessarily
follows that opaque bodies in the immediate
neighbourhood are somewhat divided and cut
away. You may see this in a familiar experiment
which I have often tried by candle-light among
my winter amusements ; if you cause a short stick
to be held out at a short distance, you will find
that as you stand apart from it, it will appear to
be serrated on both sides where the light crosses
it, as if it were cut and ragged."

2. He argues from the opticians Alhazen the
Arabian, and Vitellio, the Sarmatian, who shew
that the base of the shadow is less than the
hemisphere of its body, if the illuminating sphere

191

be greater than tliat which is illuminated ; whence
he assumes as certain that " nothing could be seen
of Mercury or Yenus in the Sun, except what
was turned away from its light and placed in the
shade; and that this must be less than half,
since the illuminated part is greater than half;
therefore Mercury, and consequently Venus,
appear to be small."

3. He gives another reason which he confesses
to be only probable : " If it be right to reason
from the analogy of the moon to other planets,
we must believe that they are not all obscure, but
have opaque parts in the middle, or nuclei, whilst
externally they are covered with a kind of trans-
parent coating like a mirror, the one part
representing the metallic foil and the other the
glass which reflects the rays that fall upon it ;
for when the moon approaches the stars, she seems
to envelope them as they draw near and to admit
them somewhat within her luminous periphery ;
on the contrary, when they are receding, she
seems to restore them to sight before they touch
her border. Moestlinus noticed this in the cases
of Mars and of the heart of the Scorpion, in the

192

year 1595 {Disput de pass. plan. Thes. 148) whence
he inferred that they are surrounded by a kind of
transparent air. But I leave this for more mature
experience."

With your leave, most learned Schickard, I
must entirely differ from you in this particular,
for I do not believe that either your Mercury or
our Venus were at all less than the true measure-
ment requires; nor are they in the heavens
different from what they appear to us in the Sun,
unless that the radiations might interfere and
increase their visible magnitude in the day time,
though this would not affect bodies seen upon the
Sun's disc. You will therefore allow me to prefer
the simple truth to your arguments which I think
may be easily confuted.

1. I readily admit that there is a remarkable,
and indeed an almost incredible, diffusion of light
when we gaze upon it with the naked eye ; and I
wish that astronomers would sufficiently bear this
in mind, and that they would not allow the false
rays of the planets and fixed stars to deceive them
by making the true magnitude of Venus and
Mercury seen in the Sun to appear so astonishing

193

owing to this delusion. Contiguous opaque bodies
are certainly divided and cut away, when beheld
by the naked eye, but not otherwise : but your
experiment of the stick seen in the candle-light,
although it may be true, does not appear to have
any reference to the point at issue : for the reason
why the light of the candle diminishes the
magnitude of the stick is because its rays are
refracted and amplified by the moisture of the
beholder's eye ; but if you look upon the shadow
of the stick upon the wall it will not be at all less
than the stick itself, unless the light be larger
than the object and the shadow be diminished at
a certain distance according to a geometrical law.
But we observed the shadows of Mercury and
Venus depicted in the light of the Sun, through
the telescope by which the rays are so modified
as to be easily endured by the eyes. Indeed if
we had tried to observe the planets in the Sun
with the naked eye, I can readily conceive that
we should not have been able to see them at all ;
for the diminutive bodies of Mercury and Venus
would have been entirely concealed from our view,
owing to the powerful light of the Sun being so

0

194

oppressive. But in a darkened view, the affair is
very different ; and there is no reason to fear the
light of the Sun diffusing itself more than is
legitimate or cutting off the contiguous opaque
bodies beyond what is proportionate.

We have a much better experiment when the
moon eclipses the Sun. The naked eye always
estimates the eclipse less than the truth, as may
be proved by many examples ; but the telescope
exhibits the exact quantity, both of the eclipse
and of the lunar diameter. I lately proved this
in the eclipse of the Sun on the 22nd of May
1639 ; and Gasendi observed the same thing in a
similar eclipse on the 11th of May 1621, when
the diameter of the moon appeared by no means
less than as observed at other times. Although
the moon when at her full seems to be enlarged
beyond her proper size, yet this is a deception
which does not occur in an eclipse of the Sun.
Moreover you yourself know the absurdity of the
dogma for reducing the semi-diameter of the new
moons, which Tycho, and after him Longomon tan us
sought to put upon us. Why then, let me ask,
do you maintain that so zealously in Mercury

195

which you properly reject as untenable in relation
to the moon ?

2. Let it be conceded to you that the Sun
illuminates more than half of the bodies of Mer-
cury and Venus, and hence, since those bodies
are precisely spherical, that they are less than half
in the shade : now in your turn you must allow
that that which, on this account, is slightly
diminished, is diminished still further from a
prior cause which deceives the eye in a most
remarkable manner. The amount is indeed so
small that it is scarcely worth naming ; but, lest
the uninformed should be misled, I will explain
how it arises : The diameter of the Sun, as seen
from the Earth, at the distance of 98,409 parts,
appeared to be 31' 30", and from Venus at the
distance of 72,000 to be 43' 3" ; but the diameter
of Venus from the Sun appears 0' 28", therefore
the angle of the cone of the shadow of Venus will
be 42' 35", which, being subtracted from the
semi-circle, leaves the circumference of the shadow
179= 17' 25", the half of which 89^ 38' 42^",
999,980,820, isthesinetotheradius 1,000, 000, 000,
and the apparent diameter of Venus is 1' 16' to

0 2

196

tlie true which is 1' 16" 0" 5"". But after all
of what consequence is a trifling difference which
does not exceed 5""? Or how can the prior
cause, which is of itself of no importance, be
deemed to increase a discrepancy which is so
small ?

But since it pleases you to debate so ingeniously,
I will reply with a similar subtlety. I deny that
the Sun illuminates more than one half, or that
the planet appears less to us from any such reason ;
on the contrary, he illuminates less than the half,
and so far are we from seeing the illuminated
portion of the hemisphere, that we cannot discern
the whole of that which is obscure, the dark part
being greater than the portion which is irradiated :
for I have no doubt that the bodies of all the
planets, and especially of Venus on account of
her strong reflection^ are mountainous and uneven
like the moon and the Earth. These mountains
therefore will obstruct the rays of the Sun so that
they cannot extend beyond the half; indeed they
will not reach over more than the half of the
mountains which intervene on every side, and
obstruct the rays of light towards the even ground.

197

This is the case as regards the Earth where the
Sun frequently conceals himself behind the moun-
tains before he reaches his true setting; and these
mountains terminate our view so that it does not
extend as far as to the middle ; accordingly the
apparent magnitude would be increased rather
than diminished thereby. But these are trifles.

3. What you advance in the third place is by
no means proved, nor do you certainly state, such
is your modesty, that the light of the Sun is
reflected from the moon and planets as from a
looking-glass. The idea is less common than
ridiculous, for the least part of a spherical glass
reflects the light of the Sun, though all surrounding
objects should remain in obscurity. It is true
that, on account of its great distance, the particle
cannot be seen, but if it could, it would appear to
be circular like the Sun ; for the same reason, the
moon never appears forked ; indeed the object
would become invisible. See a dissertation on
this question by that acute astronomer Galileo in
his Cosmic System.

Moreover the lunar mountains seen through
the telescope plainly shew, from the very dark

198

shadow which they cast, that the external surface
of the moon is not transparent. Hence it is
evident that her exterior matter is not less opaque
than that of our Earth : nor do you consider
that to entertain a contrary opinion is tacitly to
confirm the Tychonian diminution of the moon
in solar eclipses, which you elsewhere condemn
as absurd.

I have not the least doubt but that the moon
is surrounded by a kind of transparent air ; nor
do I think otherwise of the rest of the planets
whose radiation is, on that account, very likely
to be augmented. For the same reason the moon
may seem to envelope the stars before they
actually reach her edge, especially if she be seen
with the naked eye, and the star is in contact with
her lucid margin ; but if you view her with the
telescope covering the stars with a dark shade,
you will perceive that, as they approach her edge,
they very suddenly vanish. William Crabtree
and I observed this most clearly in the conjunction
of the moon and Pleiades on the evening of the
19th of March in the year 1637. These circum-
stances therefore do not by any means increase
the magnitudes of Venus or Mercury.

199

Although Mercury rising from the horizon at
Aix in Provence, together with Arcturus, on the
10th of October 1621, appeared equal to it in the
eyes of Gassendi, yet this is no disparagement to
the observation of the transit. For albeit that
star is commonly estimated 2', it is nevertheless
very properly taken by you to be much less
than 1'. Galileo found, by a singular method of
observation, that the diameter of a fixed star of
the first magnitude was not greater than 5" ; and
if the fixed stars did not shine by their own light,
they would perhaps appear to be much less : the
telescope, by which they are so much more
distinctly seen, represents them as mere points,
as was evident in the conjunction of the moon
with the Pleiades ; for as soon as the moon
covered the bodies of the stars, their false rays
immediately vanished, whereas if these had pro-
ceeded from the bodies of the stars themselves,
they would have subsided gradually and not
suddenly.

I greatly wonder that all astronomers should
have been so much deceived in computing the
diameters of the planets which they make five

200

or six, and in some instances even nine or ten
times as great as they ought to be. I think
however that I understand the cause of the error,
which is that they have not taken these adven-
titious rays into consideration. Still it surprises
me that they should all have been so negligent
as not to perceive a deception so remarkable as
to be detected even by the naked eye. For I
have often observed both Venus and Jupiter,
during the day, when the Sun's altitude was some
degrees, to be so minute that they could scarcely
be discerned, and I have, in imagination, com-
pared their diameters with those of the Sun and
moon ; but they seemed to defy all computation,
and not to equal one-hundredth part of the
diameter of the former luminary, whereas the
common opinion supposes them to be a tenth or
even a sixth or fifth. Galileo notices this error
in estimating the diameters of the planets and
fixed stars, and gives a method of measuring
them even without the aid of a telescope, which
I have frequently tried with respect to Venus,
and by which, although I may not have ascer-
tained the truth very accurately, I have discovered
the greatness of the common error.

201

On the 7th of January in the present year
1640, the Sun being risen and diminishing the
rays of Venus by his own light, an iron needle
whose diameter was 8 parts at a distance of 4300
covered the planet Venus ; therefore the diameter
was 0' 38'^

On the 29th of January in the same year, a
needle of 5 parts covered Venus at the distance
of 383 ; therefore the diameter was 0' 27".

In these observations I looked through a small
opening made with a fine needle in a piece of
card; by which method alone, even on a dark
night, the diameters of the planets appear to be
wonderfully reduced : so that, unless you are
very strong-sighted, you can scarcely discover
either the planets or the fixed stars which deceive
the naked eye from their rays being so entirely
cut ofi* by the narrow opening.

For these reasons, I have no doubt that the
diameter of Venus in the Sun appeared its proper
size, and did not differ one second from the
truth.

202

CHAPTEE XVII.

Of the Diameters of the rest of the Planets^ of the Propor-
tion of the Celestial Spheres^ and of the Parallax of
the Sun,

I SHALL here say something which may tend to
throw light upon the dimensions of the stars, and
upon the horizontal parallax of the Sun, a matter
of the greatest importance, and one which has
been the subject of much fruitless speculation ;
but I will not speak dogmatically, nor, as I may
say, ^'ex cathedra," but rather for the sake of
promoting discussion, and with the view of
examining other men's opinions.

John Kepler, the prince of astronomers,
speaking of the relative proportion of the planets
{Astr, Cop. page 484), thinks it "quite agree-
able to nature that the order of their magnitudes
and of their spheres should be the same ; that is
to say, that of the six primary planets. Mercury
should be the least, and Saturn the largest,
inasmuch as the former moves in the smallest,
and the latter in the largest orbit."

203

" But as the dimensions of their bodies may be
regarded as threefold, either according to their
diameters, their superficies, or their bulk," he is
doubtful which should be preferred. He thinks
the first proportion "to be beyond question
contrary to original reasons, as well as to the
observations made on the diameters by means of
the Belgian telescope." He advocates the second,
because the original reasons are preferable ; whilst
Remus Quiet an us, a man well versed in practical
observations, defends the third; and with him
Kepler at length agrees, retaining this proportion
in the Rudolphian tables. But as this was not
found to be entirely satisfactory, he sought a
proportion in the density of the matter, whereby
the bodies of equal magnitude may differ in
weight, and vice versa.

To give my opinion upon the subject, I am
persuaded that the proportion of the globes and
orbits of the planets is the most accurate and
certain, for such would appear the most agreeable
to the Divine Nature which formed all things by
weight and measurement, and as Plato says,
" aeternam exercet geometriam." Moreover the

204

proportion that obtains between the periods of
the motions of the planets and the semi-diameters
of the orbits is most exact, as Kepler, who dis-
covered it, very justly remarks, and as I have
accurately proved by repeated observation.
Indeed there is not an error even of a single
second. Since therefore it is true that the Sun
by its attractive power regulates the motions of
the six primary planets, I cannot conceive how
it could adapt that power so perfectly to their
several distances, unless those moveable globes
themselves were similarly proportioned. In
short, a well-conducted inspection of the diame-
ters clearly warrants the same conclusion ; neither
is it necessary with Kepler to have recourse to
material density.

What then, you will ask, is the proportion of
these orbits and bodies ? I reply, that it is the
first one which has reference to the diameters,
and which Kepler and others very inconsiderately
reject; and this proportion is more acceptable
from its suitableness, and has been more corro-
borated by my own observation than that of
either superficies or bulk.

205

For what, I ask, can be more absurd than to
compare the semi-diameter of the orbit with the
superficies or magnitude of the planet, rather than
with its semi-diameter ? It is as though we were
to compare the head of one person with the foot
of another, or as the poet says : —

" Humano capiti cervicem. pictor equinam
Jungere si velit, et varias inducere plumas
Undique coUatis membris."

But on the other hand, what can be more appro-
priate than that the diameters of the orbit and
of the planet should be proportioned to one
another ? According to this relation, both their
superficies and magnitudes should be similarly
proportioned. If Peter be twice as tall (altior)
as John, it is not necessary in order to preserve
the proportion, that his head be twice as great,
(majus) nor twice the superficies, but twice as
thick (crassius) ; and the matter will stand thus :
as the body of Peter is to the body of John, so
is the head of Peter to the head of John, in
whatever proportion, whether of thickness, {crassi-
tudinis,) or of superficies or bulk {corj)ulantiw) ;

206

and so it is with regard to the spheres. For,
because Saturn is nearly ten times taller (altior)
than the Earth, he will not therefore be ten times
greater, {major,) nor have a superficies ten times
larger ; but inasmuch as they are spheres, the
orbital diameter of Saturn will contain ten times
that of the Earth. Indeed any proportion may
be calculated in this manner ; for as the diameter,
superficies, or bulk of the sphere of Saturn is to
the diameter, superficies, or bulk of the sphere of
the Earth, so is the diameter, superficies, or bulk
of the globe of Saturn to the diameter, superficies,
or bulk of the globe of the Earth ; and so it is
with regard to the rest.

But let us pass on to notice the observations
upon which they chiefly rely who reject these
arbitrary proportions as vain. It is clear fi:*om
the example of Venus that experience is entirely
against the proportion of Kepler ; and this is also
evident from Gassendi's observation of the planet
Mercury, the diameter of which he found to be
scarcely equal to the third part of a minute,
although Kepler's calculation extends it to three
minutes. The same is the case with reference

207

to Mars whose diameter, according to Kepler's
rules, is sometimes increased beyond six minutes ;
whereas, in reality, it never equalled two : and
Kepler himself confesses that when Mars was
nearest the Earth, he did not appear much larger
than Jupiter which he estimates at only fifty
seconds. He errs less, scarcely at all, with regard
to Saturn and Jupiter.

But Kepler writes that the proportion of the
diameters is without doubt disproved by observa-
tion. I reply that he created a shadow which
prevented him from seeing clearly. It is true
that observation is opposed to it, if his parallax of
the Sun, which is of one minute, is to be taken ;
but I see no necessity for adopting such a parallax,
nor do I acknowledge the propriety of his original
speculations, much less of his other arguments.
Such reasoning is absurd, and like begging the
question; the true proportion of the orbits and
globes should be sought from observation. In this
way the apparent semi-diameter of the Earth, or
parallax of the Sun, may be concluded ; and if
this is borne out by observation the thing is
finished.

208

I say therefore that the diameter of any primary
planet, distant from the Sun 15,000 of its own
semi-diameters, must appear in the Sun near
0' 28" in mean distance. This seems to be con-
sistent with nature ; and I will shew in the case
of each of the planets that it is not contrary to
observation.

1. I will begin with Venus whose diameter I
have observed most accurately ; and, in her con-
junction with the Sun, found to be 1' 16", she
being, at the time, distant from the Earth 26,409
parts. In her mean distance therefore of 72,333
from the Sun, it appears to be nearly 0' 28".

2. The observation which Gassendi made on
the 28th of October 1631, proves almost the same
thing with respect to Mercury : he found that his
diameter in the Sun scarcely equalled twenty
seconds. The Rudolphian calculation makes the
distance of Mercury from the Earth 67,525 ;
therefore, in his mean distance from the Sun
which that calculation states to be 38,806, Mer-
cury will be nearly equal to 0' 34", which
approaches closely to 0' 28", a quantity that is
given precisely if four seconds be taken from the

209

observation, as indeed his words seem io intimate.
Thus these two planets preserve their proportion
in a remarkable manner, nor do I believe that the

rest would differ if thev could be observed as

«/

carefully ; but since we have not the like advan-
ta,ge with regard to them, we must pass on to
other methods.

3. Remus and Kepler suppose that Saturn
never exceeded thirty seconds, a conjecture which
I conceive to be very near the truth, as this planet
does not differ perceptibly in respect of distance
or diameter. At ten o'clock on the evening of
the 6th of September 1639, Saturn appeared as if
joined in longitude to a little star placed by
Tycho's catalogue in 20° i^, and he is further said
to have appeared at the back of a star of the fifth
magnitude, and rather towards the west. The
distance compared with the diameter of the moon,
was thought to be seven or eight minutes ; and
upon comparing it afterwards with the diameter
of Saturn, I was unable, owing to the great
variation, to form a precise estimate; it was
however greater than 8 to 1, and less than 16
to 1 ; Saturn therefore rather exceeded half-a-

p

210

minute, but did not equal a whole minute. All
this was ascertained by means of a telescope.

4. Kepler supposes {Astr. Cop. page 485) that
Jupiter covers about fifty seconds by twilight.
My proportion gives thirty-seven ; the difference
is not very great, and may be explained by
Jupiter's brightness which increases his appear-
ance. I have often compared Jupiter with
Venus, which may be done with certainty, as
they shine so equally. On the morning of the
25th February 1640, I thought him rather less;
on the 2nd March, I thought him equal or perhaps
rather larger ; on the 6th, I thought him evidently
larger. The diameter of Venus, at that time, was
0' 24", according to my estimate ; and that of
Jupiter about the same quantity. I do not sup-
pose that this calculation is so accurate that a
fault of a few seconds may not have arisen in it,
either from the variable altitude of the planets, or
from the degree of clearness of the diurnal light ;
but the conjecture is sufficiently satisfactory to
my own mind, since it is clear that Jupiter does
not differ perceptibly from the proportion of the
other planets.

211

5. The planet Mars loses by comparison with
the rest ; and certainly does not exceed the
assigned proportion. I suppose this is owing to
his light being so remarkably obscure, for none
of the planets sheds a feebler glow, or diffuses
fewer rays. In the beginning of the month of
March 1640, Mars appeared much less than
Jupiter, though they were in reality equal. He
emits however a stronger ray by twilight when
he is nearest to the Earth, and sometimes appears
so immensely large that he is mistaken by the
inexperienced for a new star ; on this latter
occasion he seems nearly equal to two minutes, a
quantity which perhaps he reaches; there is
however some doubt upon this point, inasmuch
as no other planet, Jupiter and Venus not ex-
cepted, actually attains this dimension, though
apparently they do not fall far short of it. But
there is no need of hesitation when others extend
the diameter to six or seven minutes; the pro-
portion here given is at all events probable, and
would doubtless agree very well with our obser-
vations, if we could make them with sufficient
accuracy. It is, without controversy, much more

212

correct than the opinions put forward by others,
which are sometimes many minutes in excess of
the truth, as may be seen by referring to the
instances of Venus and Mars.

6. Since therefore it is certain that the
diameters of the five primary planets, in mean
distance, appear from the Sun 0' 28", and that
none of them deviate from this rule, tell me, ye
followers of Copernicus, for I esteem not the
opinions of others, tell me what prevents our
fixing the diameter of the Earth at the same
measurement, the parallax of the Sun being
nearly 0' 14" at a distance, in round numbers, of
15000 of the Earth's semi-diameters ? Certainly,
if the Earth agree with the rest as to motion, if
the proportion of its orbit to that of the rest be so
exact, it is ridiculous to suppose that it should
dificr so remarkably in the proportion of its
diameter. For it is incredible that of the six
primary planets the diameter of one should be as
much as 2', or as others make it 6', whilst all the
rest should not exceed 0' 28". I have not within
reach the opinions of other astronomers ; but
every one must believe what he sees for himself,
and to me such a parallax seems absurd.

213

But it may be replied that this is merely a
probable conjecture, and has not the force of
demonstration ; and further that so immense a
distance is unbelievable, inasmuch as it exceeds,
by ten times or more, the opinions hitherto
received which so many excellent astronomers
have geometrically demonstrated from their
observations on eclipses. But I answer :

1. I do not put forth this conjecture as an
absolute demonstration, but rather as being
highly probable, and having as much weight as
many others which are carefully received in
astronomy. Who, for instance, will prove to me
that all the stars are spherical bodies ? This has
lono; been known to be true as to the Earth and
moon, and has been very recently ascertained as
to the Sun and Venus, and the fact that such is
the case with them obliges us to suppose, although
it cannot be demonstrated by experiments, that
it is so with Jupiter and Saturn, &c. ; at all
events they are not planes as they appear to be
to us. Kepler rightly concluded that the figure
of the orbits of all the planets is elHptical ; and
though this cannot be verified with respect to

214

Venus and tlie Earth, on account of tlieir small
eccentricity, it is sufficient that observations do
not disprove in their case that form which is
required in the case of others, and it is enough
that no good reason can be alleged why we
should not assign to the Earth the same propor-
tion which all other planets possess.

2. It has lately been shewn, from the diameter
of Venus, how little importance is to be attached
to the common opinion of astronomers respecting
the Sun's parallax; for though the planet was
so long open to observation, and her diameter
could have been measured by so many dilFerent
methods, it is fixed, by common consent, at least
ten times as great as it ought to be. What fear
then of innovation can arise from my stating that
the same thing has happened in respect of the
diameter of the Earth, the appearance of which
in the Sun no one ever saw, and the investigation
of which is most difficult, and has not hitherto
been properly undertaken ?

3. Moreover if any one has clearly demon-
strated from observation a greater parallax, and
does not find mine to be in all respects confirmed.

215

I am willing to reject it as a false speculation.
I know how loudly some speak of the distance of
the Sun as demonstrated from the centre of the
Earth; but they are triflers, seeking for vain
glory, and trying to impose fallacies upon the
credulous, instead of bringing forward actual
proof

I had intended to offer a more extended
treatise on the Sun's parallax ; but as the subject
appears foreign to our present purpose, and cannot
be dismissed with a few incomplete arguments, I
prefer discussing it in a separate treatise, "Z)^
syderum dimensione " which I have in hand. In
this work, I examine the opinions and views of
others ; I fully explain the diagram of Hipparchus
by which the Sun's parallax is usually demon-
strated, and I subjoin sundry new speculations ;
I also shew that the hypotheses of no astronomer,
Ptolemy not excepted, nor even Lansberg who
boasts so loudly of his knowledge of this subject,
answer to that diagram, but that Kepler alone
properly understood it ; I shew in fact that the
hypotheses of all astronomers make the Sun's
parallax either absolutely nothing, or so small

216

that it is quite imperceptible, whereas they them-
selves, not understanding what they are about,
come to an entirely opposite conclusion, a paradox
of which Lansberg affords an apt illustration.
Lastly, I shew the insufficiency and uselessness
of the common mode of demonstration from
eclipses ; I give many other certain and easy
methods of proving the distance and magnitude
of the Sun, and I do the same with regard to the
moon and the rest of the planets, adducing
several new observations.

London :—\Yertheim, Macixiosh, and Hunt, 24, Paternoster Row,
and 23, Holies Street, Cavendish Square.

v;>.'

:J^:^'

QB309.H6

3 5002 00049 0065

Horrocks, Jeremiah

Transit of Venus across the sun, a trans

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QB

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AUTHOR

iiorrocks

32884

TITLE

The transit

of venus across the

Astron

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