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24, Paternoster Row. 



In i^emoriam 


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







A. B. W. 



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 



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 


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 


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 


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 


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 


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 


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 


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 


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 


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 


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. 


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 


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 


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 


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- 

Magini Secunda MobHia. 

Mercatoris Chronologia. 

Plinii Hist. Natiiralis. 

Ptolemaei Magntim Opus. 

Regiomontani Epitome. 





J. CapitoKnus. 

Clavii Apolog. Cal. Rom. 

Clavii Comm. in Sacrobos- 

Copernici Eevolunitiones. 
Julius Firmicus. 
Gassendi Exerc. Epist in 

Phil. Fluddanam. 
Gemmae Frisii Radius As- 

ComeHi Gemmae Cosmo- 

Herodoti Hjstoria. 
J. Kepleri Astron. Optica. 

Epit. Astron. Copern. 

Com. de motu Martis. 

Tabulae Rudolpbinae. 

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

Theonis Comm. in Ptolom. 
Tyc. Brabaei Progymnas- 


Epist. Astron. 

Waltheri Observata. 


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 


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 


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 


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/' 


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 


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 



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 


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 



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 


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 


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- 

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- 


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 


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 

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 


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 


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. 


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 


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 


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 


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. 


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 


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 


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,'''' 


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 


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 


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 


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 


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 


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, 


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. 


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 


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. 


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 


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, 


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 


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 


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 


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- 

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 


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 



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 


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 


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 


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- 


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 


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. 


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 


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. 


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 


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 ; 


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 : — 


"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., 


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 


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- 


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 


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 


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 



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 



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 


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- 


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 


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 


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, 


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 

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 


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 


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 


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 


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, 


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. 





DIED IN 1641, AGED 22. 









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 


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 


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





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," 



sun's PARALLAX. 







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






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 


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 


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 


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 


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. 


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 


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 


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 


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 


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 


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 


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 


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 


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 


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- 


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 


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 


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 



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 


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 


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 


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 


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 


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 


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 


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- 


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 


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." 







On the 24th of November, 1639. 



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 


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- 


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 


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 


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 



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 


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 



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 


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 


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


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 


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 


"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 ; 


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. ! 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, 
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 


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 




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 


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 


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 

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 


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- 


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. 


What others observedy or might have observed, of this 

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


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 


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, 



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 

I wrote also of the expected transit to my 


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 



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 


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- 

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 


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 ! 

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, Venus ! and attend to 
thee ere thou dost depart. 


** 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." 



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. 


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 


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 


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. 


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 


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 


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 

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, 


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. 


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 


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. 


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 



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 : 


E O 




By the Clock. 

The Distances of the Centres. 


15' 17' 


14' 10" 


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- 



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 : 



The true situation of the 

sun . 



The right ascension . . 




The altitude of the Equator . 



From these is given 

D. M. 



D. M. 

The Hour 

3 15 



3 45 

The Culminating degree . . . 

27 34 



4 48 

The Meridian angle .... 

78 37 



76 4 

The altitude of the Culmination 

15 43 



17 18 

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

45 10 



52 24 

Therefore the angle IN" C L . . 

70 56 



67 55 

To which V C ]Sr beicg added . 

62 30 



62 30 

Gives the angle Y C L ... 

133 26 



130 25 

To the complement of which E C V 

46 34 



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 


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 


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 




















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 


The alteration of the apparent into the true situation 

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 


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 52 

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

Gives the parallax of Venus from the Sun ..038 


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, 


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- 


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 













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 


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. 


















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 ; 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 8 31 

And with the side T E 26409 





Therefore the side E Y 


2nd. In the plane S E Y 

The right angle S E Y is given 

And the side SE 


With the side E Y 


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



3rd. In the spherical triangle I^ E Y 

The right angle at E is given 

The arc EY... 



And the angle E :N" Y 



Therefore the arc KE 



Let the place of the conjunction be added to this 





Which makes the longitude of the node 





But the node of Yenus is according to 











Lansberg ... 





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 


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. 

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 


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 

Therefore the side Y M 

And the side CM 

















D. M. S. 


















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 

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 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 
































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 

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



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, 


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 


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. 


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, 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 


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, 
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 


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 


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, 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'. 


Of the Suk". 


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 10 53 
The proportional parts (scrupula propor- 


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 53 12 

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

The apogee 48 20 

The anomaly of the centre 2 55 54 29 

The prosthaphceresis of the centre to be sub- 
tracted 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 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 


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 


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


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. 


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. 


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 



38 do. do 




The ten first months of a common year 

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



Additional days in November .... 


46 16 46 of 

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



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 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 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 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 40 55 

Therefore the north latitude ofYenus . , 10 45 


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 

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. 



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. 


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- 

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 33 5 

The proportional parts (scrupula propor- 


The eccentric longitude 4 12 

The mean anomaly of the orbit 3 

The equate anomaly of the orbit .... 3 
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 







































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. 


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- 


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 ? 



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 ? ! 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, 


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- 

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 49 32 

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

The distance between the Earth and the Sun 98350 

N 2 


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 14 29 
The prosthaphoeresis of the orbit to be sub- 
tracted 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 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. 



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 


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. 


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 

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 


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. 


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- 


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. 


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 

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 


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. 



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, 


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 


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 


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 


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 


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 

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 


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 


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 


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 



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. 


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 


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. 


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 

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


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. 


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 



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." 


" 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 


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. 


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) ; 


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 


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 


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 

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 


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- 



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. 


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 


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. 


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 


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. 


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 

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 


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. 




3 5002 00049 0065 

Horrocks, Jeremiah 

Transit of Venus across the sun, a trans 








The transit 

of venus across the 














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