55Newton 1455
SrSir
In order to let you know yethe case between Mr Hook & me I gave you an
account of wtwhat past between us in orour Letters so far as I could remember. For tis long
since they were writ & I do not know that I have seen ymthem since. I am almost con
fident by circumstances that SrSir Chr. Wren knew yethe duplicate proportion wnwhen I gave him
a visit, & then Mr Hook (by his book Cometa written afterward) will prove yethe last
of us three ytthat knew it. I intended in this Letter to let you understand yethe case fully
but it being a frivolous business, I shal content my self to give you yethe heads of it
in short: vizt ytthat I never extended yethe duplicate proportion lower then to yethe superficies
of yethe earth & before a certain demonstration I found yethe last year have suspected
it did not reach accurately enough down so low: & therefore in yethe doctrine of
projectiles never used it nor considered yethe motions of yethe heavens: & consequently
Mr Hook could not from my Letters wchwhich were about Projectiles & yethe regions de
scending hence to yethe center conclude me ignorant of yethe Theory of yethe Heavens.
That what he told me of yethe duplicate proportion was erroneous, namely that it
reacht down from hence to yethe center of yethe earth. That it is not candid to
require me now to confess my self in print then ignorant of yethe duplicate pro
portion in yethe heavens for no other reason but because he had told it me in
the case of projectiles & so upon mistaken grounds accused me of that ignorance.
That in my answer to his first letter I refused his correspondence, told him I had
laid Philosophy aside, sent him only yethe experimtexperiment of Projectiles (rather shortly
hinted then carefully described) in complemtcomplement to swieeten my Answer, expected
to heare no further from him, could scarce perswade my self to answer his
second letter, did not answer his third, was upon other things, thought no
further of philosophical matters then his letters put me upon it, & therefore
may be allowed not to have had my thoughts of that kind about me so well
at that time. That by the same reason he concludes me then ignorant of
yethe duplicate proportion he may as well conclude me ignorant of yethe rest of
that Theory I had read before in his books. That in one of my papers writ
(I cannot say in what year but I am sure some time before I had any
correspondence wthwith Mr Oldenburg & that's) above fifteen years ago, the proportion
of yethe forces of yethe Planets from yethe Sun reciprocally duplicate to their distan
ces from him is exprest & yethe proportion of orour gravity to yethe Moon's conatus
recedendi a centro Terræ is calculated thô not accurately enough. That wnwhen
Hugenius put out his Horol. Oscil.Horologium Oscillatorium a copy being presented to me; in my letter of
thanks to him I gave those rules in yethe end thereof a particular commendation
for their usefulness in Philosophy, & added out of my aforesaid paper an in
stance of their usefulness in comparing yethe forces of yethe Moon from yethe earth
& earth from yethe Sun in determining a Probleme about yethe Moons phase & putting
a limit to yethe Sun's parallax. Which shews that I had then my eye upon com
paring yethe forces of yethe Planets arising from their circular motion & understood
it: so that a while after wnwhen Mr Hook propounded yethe Probleme solemnly in
yethe end of his Attempt to prove yethe motion of yethe earth, if I had not known yethe
duplicate proportion before I could not but have found it now. Between 10 &
11 years ago there was an Hypothesis of mine registred in yoryour books, wherein I hinted a
cause of gravity towards yethe earth Sun & Planets wthwith yethe dependance of yethe celestial
motions thereon: in wchwhich yethe proportion of yethe decrease of gravity from yethe superficies
of yethe Planet (thô for brevities sake not there exprest) can be no other then re
ciprocally duplicate of yethe distance from yethe center. And I hope I shall not be urged
to declare in print that I understood not yethe obvious mathematical conditions of my own Hypothesis. But
grant I received it afterwards from Mr Hook, yet have I as great a right to it
as to yethe Ellipsis. For as Kepler knew yethe Orb to be not circular but oval & guest
it to be Elliptical, so Mr Hook without knowing what I have found out since his
letters to me, can know no more but that yethe proportion was duplicate quam proximè
at great distances from yethe center, & only guest it to be so accurately & guest amiss in extending ytthat proportion down to yethe very center, whereas Kepler guest right at
yethe Ellipsis. And so Mr Hook found less of yethe Proportion then Kepler of yethe Ellipsis.
There is so strong an objection against yethe accurateness of this proportion, ytthat without
my Demonstrations, to wchwhich Mr Hook is yet a stranger, it cannot be beleived by a
judicious Philosopher to be any where accurate. And so in stating this business I
do pretend to have done as much for yethe proportion as for yethe Ellipsis & to have
as much right to yethe one from Mr Hook & all men as to yethe other from Kepler.
And therefore on this account also he must at least moderate his pretenses.
The Proof you sent me I like very well. I designed yethe whole to consist of
three books, the second was finished last summer being short & only wants transcri
bing & drawing the cuts fairly. Some new Propositions I have since thought on
wchwhich I can as well let alone. The third wants yethe Theory of Comets. In Autumn
last I spent two months in calculations to no purpose for want of a good method,
wchwhich made me afterwards return to yethe first Book & enlarge it wthwith divers Propo
sitions some relating to Comets others to other things found out last Winter. The
third I now designe to suppress. Philosophy is such an impertinently litigious
Lady that a man had as good be engaged in Law suits as come neare as have to do with her. I found it so formerly & now I no sooner come near her again but she
gives me warning. The two first books without the third will not so well
beare yethe title of Philosophiæ naturalis Principia Mathematica & therefore I
had altered it to this De motu corporum libri duo: but upon second thoughts I
retain yethe former title. Twill help yethe sale of yethe book wchwhich I ought not to diminish
now tis yorsyours. The Articles are wthwith yethe largest to be called by that name. If you
please you may change yethe word to sections, thô it be not material. In yethe first
page I have struck out yethe words uti posthac docebitur as referring to yethe third book.
Which is all at present from
YorYour affectionate friend &
humble Servant
Is: Newton.
Cambridge
June 20. 1686.
Since my writing this letter I am told by one who had it from another
lately present at one of yoryour meetings, how that Mr Hook should there make a great
stir pretending I had all from him & desiring they would see that he had justice
done him. This carriage towards me is very strange & undeserved, so that I
cannot forbeare in stating ytthat point of justice to tell you further, that he has published Borell's Hypothesis in
his own name & the asserting of this to himself & completing it as his own, seems
to me the ground of all yethe stir he makes. Borel did something in it & wrote
modestly, he has such a way done nothing & yet written in such a way as if
he knew & had sufficiently hinted all but what remained to be determined by yethe
drudgery of calculations & observations, excusing himself from that labour by reason
of his other business: whereas he should rather have excused himself by reason of
his inability. For tis plain by his words he knew not how to go about it. Now
is not this very fine? Mathematicians that find out, settle & do all the business
must content themselves with being nothing but dry calculators & drudges & another
that does nothing but pretend & grasp at all things must carry away all the invention as55– as well of those that were to follow him as of those that went before. Much after
the same manner were his letters writ to me, telling me that gravity in descent
from hence to yethe center of yethe earth was reciprocally in a duplicate ratio of yethe
altitude, that yethe figure described by projectiles in this region would be an Ellipsis
& that all yethe motions of yethe heavens were thus to be accounted for: & this he did
in such a way as if he had found out all & knew it most certainly. And
upon this information I must now acknowledge in print I had all from him & so
did nothing my self but drudge in calculating demonstrating & writing upon
yethe inventions of this great man. And yet after all, the first of those three
things he told me is fals & very unphilosophical, the second is as fals & yethe
third was more then he knew or could affirm me ignorant of by any
thing that past between us in orour letters. Nor do I understand by wtwhat right he
claims it as his own. For as Borell wrote long before him that by
a tendency of yethe Planets towards yethe sun like that of gravity or magnetism
the Planets would move in Ellipses, so Bullialdus wrote that all force re
specting yethe Sun as its center & depending on matter must be reciprocally
in a duplicate ratio of yethe distance from yethe center, & used that very
argument for it by wchwhich you, SrSir, in the last Transactions have proved
this ratio in gravity. Now if Mr Hook from this general Proposition in Bul
lialdus might learn yethe proportion in gravity, why must this proportion here
go for his invention? My letter to Hugenius wchwhich I mentioned above was directed to Mr Oldenburg
who used to keep yethe Originals. His papers came into Mr Hooks possession. Mr
Hook knowing my hand might have yethe curiosity to look into that letter & thence
take yethe notion of comparing yethe forces of yethe Planets arising from their circular
motion & so what he wrote to me afterwards about yethe rate of gravity, might
be nothing but yethe fruit of my own Garden. And its more then I can affirm ytthat yethe
duplicate proportion was not exprest in that letter. However he knew it not (ias I gather from
his books) till five years after any Mathematician could have told it him. For when
Hugenius had told how to find yethe force in all cases of circular motion, he
had told 'emthem how to do it in this as well as all others. And so yethe honour of doing
it in this way is due to Hugenius. For another five years after to claim it as his own
invention, is as if some Mechanick who had learnt yethe Art of surveying from a
Master should afterwards claim the surveying of this or that piece of ground
for his own invention & keep a heavy quarter to be in print for 'tit. But what if
this surveyor be a bungler & give in an erroneous survey? Mr Hook has erred
in the invention he pretends to & his error is yethe cause of all the stirr he makes.
For his extending yethe duplicate proportion down to yethe center (which I do not)
made him correct me & tell me yethe rest of his Theory as a new thing to me
& now stand upon it that I had all from that his letter: notwithstanding that
he had told it to all yethe world before & I had seen it in his printed books
all but yethe proportion. And why should I record a man for an Invention who
founds his claim upon an error therein & on that score gives me trouble? He
imagins he obliged me by telling me his Theory, but I thought my self disobli
ged by being upon his own mistake corrected magisterially & taught a Theory
wchwhich every body knew & I had a truer notion of then himself. Should a man
who thinks himself knowing, & loves to shew it in correcting & instructing others,
come to you when you are busy, & notwithstanding your excuse, press discourses
upon you & through his own mistakes pr correct you & multiply discourses &
then make this use of it, to boast that he taught you all he spake & oblige
you to acknowledge it & cry out injury & injustice if you do not, I beleive
you would think him a man of a strange unsociable temper. Mr Hooks letters
in several respects abounded too much wthwith that humour wchwhich Hevelius & others
complain of & therefore he may do well in time to consider whether after this new provocation I be much more bound (in doing him that justice he claims) to make an honourable mention of him in print, especially since this is yethe third time that he has given
me trouble in this kind.
For your further satisfaction in this business, I beg yethe favour you would con
sult yoryour books for a paper of mine entitled, An Hypothesis explaining yethe properties of light. TwasIt was dated Decemb. 7th 1675 & registred in your Book about
Ian or Feb following. Not far from yethe beginning there is a Paragraph ending
wthwith these words. And as yethe Earth so perhaps may the Sun imbibe this spirit copi
ously to conserve his shining & keep yethe Planets from receding further from him
& they that will may also suppose that this spirit affords or carries thither the solary
fewel & materiall principle if light: And that yethe vast ethereal spaces between
us & yethe stars are for a sufficient repository for this food if yethe Sun & Planets.
But this if yethe constitution if ethereal natures by yethe by. In these & yethe foregoing
words you have yethe common cause of gravity towards yethe earth Sun & all the
Planets, & that by this cause yethe Planets are kept in their Orbs about yethe Sun.
And this is all yethe Philosophy Mr Hook pretends I had from his letters some
years after, the duplicate proportion only excepted. The preceding words contein
yethe cause of yethe phænomena of gravity as we find it on yethe surface of the earth
without any regard to yethe various distances from yethe center: For at first I designed
to write of nothing more. Afterwards, as my manuscript shews, I interlined yethe
words above cited relating to yethe heavens, & in so short & transitory an inter
lined hint of things, the expression of yethe proportion may well be excused.
But if you consider yethe nature of yethe Hypothesis you'l find that gravity decreases upward & can be no other
from yethe superficies of yethe Planet then reciprocally duplicate of yethe distance from
the center, but downwards that proportion does not hold. This was but an
Hypothesis & so to be looked upon only as one of my guesses which I did not
rely on: but it sufficiently explains to you why in considering yethe descent of a
body down to yethe center I used not yethe duplicate proportion. In yethe small
ascent & descent of projectiles above yethe earth yethe variation of gravity is so
inconsiderable ytthat Mathematicians neglect it. Hence yethe vulgar Hypothesis with
them is uniform gravity. And why might not I as a Mathematician use it fre
quently without thinking on yethe philosophy of yethe heavens or beleiving it to be
philosophically true?
For Mr Edmund Halley.
Mr Newton of
June 20o 1686