_First_, that the Waters of the _Nile_ are Nitrous, explicating the Nature
of Salt, and Saltpeter, and imputing the fertility of the Earth, as well us
the fecundity of Animals, to Salt. Where he shews, that all things, that
serve to improve Land, are full of Salt; and that 'tis observ'd, that grain
steep'd in Vrine, before sowing, rises sooner, and becomes fuller and
stronger, than else. Adding, that that, which renders the Seed of Animals
prolifick, is, that one of the _Spermatick_ veins hath its Origine from the
_Emulgent_, through which the Nitrous and Saline Serosities, that discharge
themselves into the Kidneys and Bladder, do pass.
In the _Second_, he examins, what is Fermentation, and how 'tis perform'd;
affirming, that, what thrusts forth Plants in the Spring, is, that the
Earth being fermented by the _Niter_, it harbours, the Nitrous spirits
insinuate themselves into their Pores.
In the _Third_ he treats of all the Circumstances, observable in the
Inundation of the Nile. 'Tis affirm'd, that 3 or 4 days before that River
begins to overflow, all its water is troubled: that then there falls a
certain Dew, which hath a fermenting vertue, and leavens a Paste exposed to
the Air: that the Mud, which has been drawn out of the water, grows
heavier, when the overflowing begins, then it was before, and that by the
increase of the weight of that Mud, they judge of the greatness of the
approaching inundation. The Author pretends, that {252} the Niter, which
the _Nile_ is stored with, is the cause of all these strange effects, and
of many others, by him alledged. For, _saith he_, when the Nitre is heated
by the heat of the Sun, it ferments, and mingling with the water, troubles
it, and swells it, and makes it pass beyond its banks; after the same
manner, as the Spirits in new Wine render it troubled, and make it boyle in
the vessel. And it seems not likely to him, that the Mud, found in the
_Nile_, should come a far off; for then it would at last so raise the banks
of this River, that it would not be able to overflow them any longer.
Whereas 'tis more than 2000 years, that the banks thereof are not grown
higher, there being now requisite but 16. cubits for overflowing the Land,
no more than there was in the time of _Herodotus_. Which shews, _saith he_,
that this Mud is nothing but a volatil _Niter_, which exhaling, doth not
increase the Earth. As for the _AEgyptian_ Dew, and the increase of the
weight of the Mud, he adscribes them to the same Cause. For the spirits of
Nitre abounding in the _Nile_, when raised into the Air with the vapors,
that exhale continually from this River, there is made out of their
mixture, a Dew, that refreshes the Air, makes sickness to cease, and
produces all those admirable effects, that make the _AEgyptians_ wish for it
so passionately. And the same spirits of Niter, being joyned to the Paste,
and to the Mud, raise the one, and augment the weight of the other. That,
which Mr. _Buratini_ observes, that at the time of this inundation, the
Niter-pits of the neighboring places vomit out liquid Niter, and that one
may see issue out of the Earth abundance of Chrystals of Nitre, is alledged
to fortify this conjecture; Which is yet more confirm'd by the Fertility,
communicated to the Earth by the Mud of this River. For, plants do grow
there in such abundance, that they would choak one another, if it were not
remedied by throwing Sand upon the Fields; insomuch that the _AEgyptians_
must take as much pains to spread Sand to lessen the fatness of their Land,
as other Nations do, to spread dung or other manure upon theirs to increase
the fatness.
In the _Fourth_ and _Fifth_, the Author undertakes to prove, that all those
strange effects cannot be attributed to Rain or Snow, {253} and that the
overflowing of the _Nile_ always happens at a certain day.
In the _Last_, he alledges some Relations, serving to confirm his Opinion;
Which are too long here to insist upon.
_DE PRINCIPIIS ET RATIOCINATIONE GEOMETRARUM, Contra Fastum Professorum
Geometriae;_ Authore _Thoma Hobbes_. It seems, that this Author is angry
with all Geometricians, but himself; yea he plainly saith in the dedication
of his Book, that _he invades the whole Nation of them_; and unwilling, it
seems, to be call'd to an account for doing so; He will acknowledge no
judge of _this_ Age; but is full of hopes, that posterity will pronounce
for him. Mean while he ventures to advance this _Dilemma_; _Eorum qui de
iisdem rebus mecum aliquid ediderunt, aut solus insanio Ego, aut solus non
insanio; tertium enim non est, nisi (quod dicet forte aliquis) insaniamus
omnes._ Doubtless, one of these will be granted him.
As to the Book it self, he professes, that he doth not write it against
_Geometry_, but _Geometers_; and that his design in it is, to shew, That
there is no less uncertainty and falsity in the writings of
_Mathematicians_, than there is in those of _Naturalists_, _Moralists_,
&c., though he judges, that _Physicks_, _Ethicks_, _Politicks_, if they
were well demonstrated, would be as certain as the _Mathematicks_.
Attacking the Mathematical Principles as they are found in Books, and
withall some Demonstrations, he takes to task _Euclid_ himself, instead of
all, as the Master of all Geometricians, and with him his best interpreter,
_Clavius_, examining in the _First_ place, the _Principles_ of _Euclid_:
_Secondly_, Declaring false, what is superstructed upon them, whether by
_Euclid_, or _Clavius_, or any _Geometer_ whatsoever that hath made use of
those or other (as he is pleased to entitle them) _false_ Principles.
_Thirdly_, Pretending, that he means so to combat all, both Principles and
Demonstrations, undertaken by him, as that he will substitute better in
their room, least he should seem to undermine the Science it selfe. {254}
The particulars, which he undertakes to reform, are,
_Punctum._
_Linea._
_Terminus._
_Linea Recta._
_Superficies._
_Superficiei Termini._
_Superficies Plana,_
_Angulus_ (Where he is large upon the _Angulus Contactus._)
_Petitio prima Elem. 1. Euclidis._
_Ratio._
_Radix & Latus._
_Prop. 16. El. 3._
_Dimensio Circuli._
_Magnitudo Circuli Hugeniana._
_Sectio Anguli._
_Ratio, quam habet recta composita ex Radio & Tangente 30. grad, ad
Radium ipsum._
_Propos. 47ae. Elem. 1. Demonstratio._
_Addita est Appendix de Mediis proportionalibus in genere._
_KING SALOMONS POUTRAITURE OF OLD AGE_; by _John Smith_, M.D. This Treatise
being a _Philosophical_ Discourse, though upon a _Sacred_ Theme, may
certainly claim a place among _Philosophical_ Transactions. Not here to
mention the many other learned Notes, this Worthy Author gives upon that
Hieroglyphical Description of Old Age, made by that Royal Pen-man of
_Ecclesiastes_, cap. 12. We shall onely take notice of that surprizingly
Ingenious one, there to be met with, concerning the Antiquity of the
Doctrine of the _Blood's Circulation_: King _Salomon_, who lived neer 2700
years agoe, using such expressions, as may, to a considering Reader, very
probably denote the same Doctrine, which the Sagacious Dr. _Harvey_ has of
late years so happily brought to light, and introduced into all the most
Ingenuous Societies of Learned men: The _Pitcher_, mention'd in the quoted
place, being Interpreted for the _Veines_, and the _Fountain_ for the
_Right Ventricle of the Heart_, as the _Cistern_ for the _Left_; the
_Wheele_, there spoken off, manifestly importing a _Circulation_, made by
the _Great Artery_ with its Branches, the principal Instrument thereof.
* * * * *
Printed with Licence for _John Martyn_, and _James Allestry_, Printers to
the Royal Society. 1666.
{255}
* * * * *
_Num._ 15.
PHILOSOPHICAL
_TRANSACTIONS._
* * * * *
_Wednesday_, _July_ 18. 1666.
* * * * *
The Contents.
_A new Experiment, shewing, How a considerable degree of Cold may be
suddenly produced without the help of _Snow_, _Ice_, _Haile_, _Wind_,
or _Niter_, and that at any time of the year. An Account of two Books,
lately printed in _London_; whereof the one is entituled, _EUCLIDIS
ELEMENTA GEOMETRICA, novo ordine ac Methodo demonstrata_; the Author
_Anonymus_. The other, _THE ENGLISH VINE-YARD VINDICATED_, by _JOHN
ROSE_._
* * * * *
_A new Frigorifick Experiment shewing, how a considerable degree of _Cold_
may be suddenly produced without the help of _Snow_, _Ice_, _Haile_,
_Wind_, or _Niter_, and that at any time of the year._
This subject will it self, 'tis presumed, without any other _Preamble_,
speak the Cause, why this present Paper is publish't at this (unusual) time
of the Month: though, by the by, it may not be amiss to add on this
occasion, that the Publisher of these _Tracts_ never meant so to confine
himself to a _Set_ time, as not to retain the Liberty of taking any other,
when there is occasion. And there being one given him, before another Month
is come in, he does without any scruple or delay comply therewith,
presenting the Curious with an Experiment which he thinks is both
seasonable, and will not be unwellcome to them; furnish't out of the Ample
Magazin of that Philosophical Benefactor, the Noble Mr. _Boyle_; Concerning
which, thus much is further thought requisite to intimate on this occasion,
that it, and some others of the same Gentlemans, that have been, and may
be, mentioned in the _Transactions_, belong to certain Treatises, the
Author hath lying by him; but that yet he denys not {256} to communicate
them to his Friends, and to allow them to dispose thereof, upon a hope,
that equitable Readers will be ready to excuse, if hereafter they should
appear also in the Treatises they belong to, since he consents to this
Anticipation, but to comply with those, that think the imparting of real
and practical Experiments, may do the Publick some Service, by exciteing
and assisting mens Curiosity in the interim.
As for the Experiment, you saw the other day at my Lodgings, though it
belongs to some Papers about _Cold_, that (you know) could not be
Publish't, when the rest of the _History_ came forth, and therefore was
reserved for the next _Edition_ of that Book; yet the Weather having been
of late very hot, and threatning to continue so, I presume, that to give
you here in compliance with your Curiosity an Account of the Main and
Practical part of the Experiment, may enable you to gratify not onely the
Curious among your Friends, but those of the Delicate, that are content to
purchase a Coolness of Drinks at a somewhat chargeable rate.
You may remember, that the Spring before the last, I shew'd you a
particular Account of a way, wherein by a certain substance obtain'd from
_Sal Armoniack_, I could presently produce a considerable degree of _Cold_,
and that with odd Circumstances, without the help of _Snow_, _Ice_, _Niter_
&c. But that Experiment being difficult and costly enough, and design'd to
afford men _Information_, not _Accomodations_, I afterwards tryed, what
some more cheap and facile mixtures of likely Bodies with _Sal Armoniack_
would do towards the Production of Cold, and afterwards I began to
consider, whether to that purpose alone (for my first experiment was
design'd to exhibite other _Phaenomena_ too) those mixtures might not
without inconvenience be omitted: and I was much confirm'd in my
conjecture, by an accident, which was casually related to me by a very
Ingenious Physician of my acquaintance, but not to be repeated to you in
few words, though he complain'd, he knew not what to make of it.
Among the several ways, by which I have made infrigidating Mixtures with
_Sal Armoniack_, the most simple and facile is this; Take one pound of
powder'd _Sal Armoniack_ and about three Pints (or pounds) of Water, put
the Salt into the Liquor, _either_ altogether, if your design be to produce
an intense, though {257} but a short coldness; _or_ at two, three, or four
several times, if you desire, that the produced coldness should rather last
somewhat longer than be so great. Stirre the powder in the Liquor with a
stick or whalebone (or some other thing that will not be injur'd by the
fretting Brine, that will be made) to hasten the dissolution of the Salt;
upon the quickness of which depends very much the intensity of the Cold,
that will ensue upon this Experiment. For the clearing up whereof, I shall
annex the following particulars.
[Sidenote: * _In the History of Cold._]
1. That a considerable degree of Cold is really produced by this operation,
is very evident: _First_ to the touch; _Secondly_, by this, that if you
make the Experiment (as for this reason I sometimes chuse to do) in a
Glass-Body or a Tankard, you may observe, that, whilst the Solution of the
Salt is making, the outside of the Metalline Vessel will, as high as the
mixture reaches within, be bedew'd (if I may so speak) with a multitude of
little Drops of Water as I have * elsewhere shown that it happens, when
mixtures of Snow and Salt, being put into Glasses or other Vessels, the
aqueous vapors that swim to and fro in the Air, and chance to glide along
the sides of the Vessels, are by the coldness thereof condens'd into Water.
And in our Armoniack Solution you may observe, that if you wipe off the Dew
from any particular part of the outside of the Vessel, whilst the solution
does yet vigorously goe on, it will quickly collect fresh Dew, which may be
sometimes copious enough to run down the sides of the Vessel. But
_Thirdly_, the best and surest way of finding out the Coldness of our
Mixture is that, which I shew'd you by plunging into it a good seal'd
Weatherglass furnish't with tincted Spirit of Wine. For the Ball of this
being put into our frigorifick mixture, the Crimson Liquor will nimbly
enough descend much lower, than when it was kept either in the open Air, in
common Water, of the same temper with that, wherein the _Sal Armoniack_ was
put to dissolve. And if you remove the Glass out of our Mixture into common
water, the tincted Spirit will, (as you may remember, it did) hastily
enough reascend for a pretty while, according to the greater or lesser
time, that it continued in the _Armoniack_ Solution. And this has succeeded
with me, when instead of removing the Mixture into _Common_ Water, I
removed it into water newly impregnated with _Salt-peter_.
{258}
2. The _Duration_ of the Cold, produc'd by this Experiment, depends upon
several Circumstances; as _First_, upon the Season of the year, and present
temperature of the Air; For, in Summer and Hot weather the Cold will sooner
decay and expire. _Secondly_, upon the Quantity of Salt and Water: For, if
both these be great, the effect will be as well more lasting, as more
considerable. _Thirdly_, for ought I yet know, we may here add the Goodness
& Fitness of the particular parcel of Salt, that is imploy'd; for, though
it be hard to discern beforehand, which will be the more, and which the
less proper; yet some trials have tempted me to suspect, that there may be
a considerable disparity, as to their fitness to produce Cold, betwixt
parcels of Salt, that are without scruple look't upon as Sal Armoniack: Of
which difference it were not perhaps very difficult to asign probable
reasons from the Nature of the Ingredients of this compound Concrete, and
the wayes of preparing it. But the Duration of the Cold may be conceived to
depend also. _Fourthly_, upon the Way of putting in the Salt into the
Water. For, if you cast it in all at once, the Water will sooner acquire an
intense degree of Coldness, but it will also the sooner return to its
former temper; Whereas, if you desire but an inferiour degree of that
Quality, but that may last longer (which wil usually be the most convenient
for the Cooling of Drinks), then you may put in the Salt by little and
little. For, keeping a long Weather-glass for a good while in our
impregnated Mixture, I often purposely try'd, that, when the tincted liquor
subsided but slowly, or was at a stand, by putting in, from time to time, 2
or 3. spoonfuls of fresh Salt, and stirring the Water to quicken the
Dissolution, the Spirit of Wine would begin again to descend, if it were at
a stand or rising, or subside much more swiftly than it did before. And if
you would lengthen the Experiment, it may not be amiss, that part of the
Sal Armoniack be but grosly beaten, that it may be the longer in
dissolving, and consequently in Cooling the Water. Whilst there are dewy
drops produced on the outside of the Vessel, 'tis a sign, that the Cold
within continues pretty strong; for when it ceases, these drops especially
in warm weather, will by degrees vanish. But a _surer_ way of measuring the
duration of the Cold, is, by removing from time to time the Seal'd
Weather-glass out of the Saline Mixture into the same common Water, with
part of which it was made. And though it be not easie to determin any thing
particularly about this matter; yet it may somewhat assist you in your
Estimates, to be inform'd, That I have in the Spring by a good
Weather-glass found a sensible adventitious Cold made by a pound of Sal
Armoniack at the utmost, to last about 2 or 3 hours.
3. To cool Drinks with this Mixture, you may put them in _thin_ Glasses,
the thinner the better; which (their orifices being stopp'd, and still kept
above the Mixture) may be moved to and fro in it, and then be immediately
pour'd out to be drunk: Though when in the Glass, I imployed, was
conveniently shap'd as, like a Sugar-loaf, or with a long Neck, I found it
not amiss to drink it out of that, without pouring it into any other; which
can scarce be done without lessning the Coolness. The refrigeration, if the
Glass viall be convenient, is quickly perform'd: And if one have a mind to
cool his hands, he may readily do it by applying them to the outside of the
Vessel, that contains the refrigerating Mixture; by whose help, pieces of
Chrystal, or Bullet for the cooling of {259} the Mouths or Hands of those
patients, to whom it may be allow'd, may be potently cool'd, and other such
refreshments may be easily procur'd.
4. How far Sal Armoniack, mingl'd with Sand or Earth, and not dissolv'd,
but only moistn'd with a little Water sprinkl'd on it, will keep Bottles of
Wine or other liquors more coole, than the Earth or that Sand alone will
do, I have not yet had opportunity by sufficient trials fully to satisfie
my self, and therefore resign that Enquiry to the Curious.
5. For the cooling of Air, and Liquors, to adjust Weather-glasses (to be
able to do which at all times of the year, was one of the chief aimes, that
made me bethink my self of this Experiment;) or to give a small quantity of
Beer &c. a moderate degree of coolness, it will not be requisite, to employ
neer so much as a whole pound of Sal Armoniack at a time. For, you may
easily observe by a seal'd Weather-glass, that a very few ounces, well
pouder'd and nimbly dissolv'd in about 4. times the weight of Water, will
serve well enough for many purposes.
6. And that you may the less, scruple at this, I shall tell you, that even
before and after Midsummer, I have found the Cold producible by our
Experiment to be considerable and useful for refrigerating of Drinks, &c.
but if the Sal Armoniack be of the fittest sort (for I intimated above,
that I suspected, 'tis not equally good) and if the season of the year do
make no disadvantagious difference, the degree of Cold, that may be
produced by no more than one pound (if not by less) of Sal Armoniack, may,
within its own Sphere of Activity, be much more vehement, than, I presume,
you yet imagine, and may afford us excellent Standards to adjust seal'd
Weather glasses by; and for several other purposes, For I remember that in
the Spring, about the end of _March_, or beginning of _April_, I was able
with one pound of Sal Armoniack, and a requisite proportion of Water, to
produce a degree of Cold much greater, than was necessary the preceding
Winter, to make it frosty Weather abroad; nay I was able to produce real
Ice in a space of time, almost incredibly short. To confirm which
particulars, because they will probably seem strange to you, I will here
annex the Transcript of an entry, that I find in a Note book of the
_Phaenomena_ and success of one of those Experiments, as I then tryed it;
though I should be asham'd to expose to your perusal a thing so rudely
pen'd; if I did not hope, you would consider, that 'twas hastily written
onely for my own Remembrance. And that you may not stop at any thing in the
immediately annext Note, or the two, that follow, it will be requisite to
premise this Account of the seal'd Thermoscope; (which was a good one)
wherewith these Observations were made; That the length of the Cylindrical
pipe was 16. Inches; the Ball, about the bigness of a somewhat large
Walnut, and the Cavity of the Pipe by guess about an eight or ninth part of
an inch Diameter.
The First Experiment is thus registered. _March_ the 27th, in the Seal'd
Weather glass, when first put into the Water, the tincted Spirit rested at
8-5/8 inches; being suffered to stay there a good while, and now and then
stirr'd to and fro in the Water; it descended at length a little beneath
7-5/8 inches; then the _Sal Armoniack_ being put in, within about a quarter
of an hour or a little more it descended to 2-11/16 inches, but before that
time, in half a {260} quarter of an hour it began manifestly to freeze the
vapours and drops of water on the outside of the Glass. And when the
frigorifick power was arriv'd at the height, I several times found, that
water, thinly plac'd on the outside, whilst the mixture within was nimbly
stirr'd up and down, would freeze in a quarter of a minute (by a
Minute-watch.) At about 3/4 of an hour after the infrigidating Body was put
in, the Thermoscope, that had been taken out a while before, and yet was
risen but to the lowest freezing mark, being again put in the liquor, fell
an inch beneath the mark. At about 21/2 houres from the first Solution of the
Salt I found the tincted liquor to be in the midst between the freezing
marks, whereof the one was at 51/2 inches (at which height when the Tincture
rested, it would usually be, some, though but a small, frost abroad;) and
the other at 43/4 inches; which was the height, to which strong and durable
Frosts had reduced the liquor in the Winter. At 3 hours after the beginning
of the Operation, I found not the Crimson liquor higher than the upper
Freezing mark newly mention'd; after which, it continued to rise very
slowly for about an hour longer; beyond which time I had not occasion to
observe it.
Thus far the _Note-book_; wherein there is mention made of a Circumstance
of some former Experiments of the like kind, which I remember was very
conspicuous in this newly recited. For, the frigorifick mixture having been
made in a Glass body (as they call it) with a large and flattish bottom, a
quantity of water, which I (purposely) spilt upon the Table, was by the
operation of the mixture within the Glass, made to freeze, and that
strongly enough, the bottom of the Cucurbite to the Table; that stagnant
liquor being turn'd into solid ice, that continued a considerable while
unthaw'd away, and was in some places about the thickness of a half Crown
piece.
Another Observation, made the same Spring, but less solemn, as meant
chiefly to shew the Duration of Cold in a high degree, is recorded in these
terms: The first time, the Seal'd Weather-glass was put in, before it
touch'd the common water, it stood at 8-1/8, having been left there a
considerable while, and once or twice agitated the water, the tincted
liquor sunk but to 7-7/8, or at furthest, 7-6/8; then the frigorifick
liquor being put into the water with circumstances disadvantagious enough
in (about) half a quarter of an hour the tincted liquor fell beneath 33/4,
and the Thermoscope, being taken out, and then put in again, an hour after
the water had been first infrigidated subsided beneath 5 inches, and
consequently within 1/4 of an inch of the mark of the strongly freezing
weather.
7. Whereas the grand thing, that is like to keep this Experiment from being
as generally _Useful_, as perhaps it will prove _Luciferous_, is the
Dearness of Sal Armoniack, two things may be offered to lessen this
Inconvenience. For _first_, Sal Armoniack might be made much cheaper, if
instead of fetching it beyond-sea, our Country-men made it here at home;
(which it may easily be and I am ready to give you the Receipt, which is no
great Secret.) But _next_, I considered, that probably the infrigidating
vertue of our mixture might depend upon the peculiar Texture of the Sal
Armoniack whereby, whilest the Water is dissolving it, either some
Frigorifick particles are extricated and excited or (rather) some particles
which did before more agitate the minute parts of the water, are expell'd
(or invited out by the ambient Bodies) or {261} come to be clogg'd in their
motion: Whence it seem'd reasonable to expect that upon the Reunion of the
Saline particles into such a Body, as they had constituted before, the
redintegrated Sal Armoniack having, neer upon, the same Texture, would,
upon its being redissolv'd, produce the same, or a not much inferior degree
of Coldness: And hereupon, though I well enough foresaw that an Armoniack
solution, being boyl'd up in Earthen vessels (for Glass ones are too
chargeable) would, by piercing them, both lose some of the more subtle
parts, and thereby somewhat impaire the texture of the rest; yet I was not
deceiv'd in Expecting, that the dry Salt, remaining in the pipkins, being
redissolv'd in a due proportion of water, would very considerably
infrigidate it; as may further appear by the Notes, which for your greater
satisfaction you will find here subjoyn'd, as soon as I have told you,
that, though for want of other vessels I was first reduc'd to make use of
Earthen ones, and the rather, because some Metallin Vessels will be injur'd
by the dissolv'd Sal Armoniack, if it be boyl'd in them; yet I afterwards
found some conveniencies in Vessels of other Mettall, as of Iron; whereof
you may command a further Account.
_March_ the 29th, the Thermoscope in the Air was at 8-7/8 inches; being put
into a somewhat large evaporating glass, fill'd with water, it fell (after
it staid a pretty while, and had been agitated in the liquor) to 8. inches:
then about half the Salt, or less, that had been used _twice_ before, and
felt much less cold than the water, being put in and stirr'd about, the
tincted Spirit subsided with a visible progress, till it was faln
manifestly beneath 4. inches; and then, having caused some water to be
freshly pump'd and brought in; though the newly mention'd Solution were
mixt with it, yet it presently made the Spirit of Wine manifestly to ascend
in the Instrument, much faster, than one would have expected, &c.
And this much may suffice for this time concerning our _Frigorifick_
Experiment; which I scarce doubt but the _Cartesians_ will lay hold on as
very favourable to some of their Tenents; which you will easily believe, it
is _not_ to the Opinion, I have elsewhere oppos'd, of those Modern
Philosophers, that would have _Salt-petre_ to be the _Primum Frigidum_:
(though I found by trial, that, whilst 'tis actually dissolving, it gives a
much considerabler degree of Cold, than otherwise.) But about the
Reflexions, that may be made on this Experiment, and the Variations, and
Improvements & Uses of it, though I have divers things lying by me; yet,
since you have seen several of them already, and may command a sight of the
rest, I shall forbear the mention of them here, not thinking it proper, to
swell the bulk of this Letter with them.
* * * * *
_An Account of two Books lately printed in London._
I. _EUCLIDIS ELEMENTA GEOMETRICA, novo ordine ac methodo demonstrata._ In
this compendious and pretty Edition, the Anonymous Author pretends to have
rendred these Elements more expeditious; by bringing all together into one
place, what belongs to one and the same subject: Comprising 1. what
_Euclid_ hath said of _Lines_, Streight, Intersecting one another, and
Parallel. 2. What he hath demonstrated of a _Single Triangle_, and of
_Triangles Compared_ one with another. 3. What of the _Circle_, and its
Properties. 4. What of _Proportions_ in Triangles and other Figures. 5.
What of _Quadrats_ and _Rectangles_, made of Lines diversly {262} cut. 6.
What of _Plane Superficies_'s. 7. What of _Solids_. After which follow the
_Problems_. The _Definitions_ are put to each _Chapter_ as need requireth.
The _Axioms_, because they are few, and almost every where necessary, are
not thus distributed in _Chapters_. The _Postulata_, are not subjoyn'd to
the _Axioms_, but reserv'd for the _Problems_, the Author esteeming, that
they being _practical_ Principles, had only place in _Problems_.
This for the _Order:_ As to the _Manner_ of Demonstrating, One and the same
is observ'd in most Propositions; all with much brevity; to the end, that
what is not of it self difficult, may not be made so, by multitude of Words
and Letters.
II. _THE ENGLISH VINE-YARD VINDICATED._ The Author (Mr. _John Rose_, his
Majesties Gardener at his Royal Garden in St. _James_'s) makes it his
business in this small Tract (a very thin Pocket-book) by a few short
Observations made by himself, to direct _Englishmen_ in the _Choice_ of the
_Fruit_, and the _Planting_ of Vine-yards; heretofore very frequently
cultivated, though of late almost quite neglected by them.
He discourses skilfully, 1. Of the _severall sorts_ of _Vines_, and what
_Grapes_ are most sutable to the _Climate_ of _England_; where he chiefly
commends the small _Black-grape_, or _Cluster-grape_; the _Parsley-grape_;
the White _Muscadine_; the _Frontiniack_; and a new _White-grape_, with a
red Wood and a dark green Leaf: All these being early ripe fruit. 2. Of the
_Soyle_, and _Scituation_ of a Vine-yard in _England_: Where, as to the
_First_, he pitches upon a _Light Soile_, having a bottom of _Chalk_ or
_Gravel_, and given to _Brambles_ observing, that no Plant whatsoever is so
connatural to the Vine for Soyl, as the _Bramble_. As for the _Scituation_
he chooses that side or declivity of a Hill, that lies to the _South_ or
_Southwest_; and is favoured with _other Hills_ somewhat higher, or _Woods_
on the _North_ and _East_, to break the rigour of those quarters. This
direction he thinks of that importance, that he affirms, that the
discouragement of the Culture of Vines in _England_ has only proceeded from
men's misinformation on this material article of _Choice_ of _Soyle_ and
_Scituation_. 3. How to _prepare_ the Ground for the Plantation, _vid._ by
plowing up the _Swarth_ in _July_, and by disposing the _Turf_ in _small_
heaps, and so burning them, and spreading the ashes over the Land; care
being taken, that by heaping too much materials together, the Earth be not
over-burnt by the excessive heat and fire, which they require to reduce
them to ashes.
What is added, of the Manner of planting the _Sets_; of Dressing, Pruning,
and Governing the Plantation; of the Ordering and Cultivating the Vine-yard
after the first four years, till it needs renewing; as also of the _manner_
and _time_, how and when to manure the Vine-yard, with Compost, will be
better understood from the Book it self, than can be here described; the
Author pretending, that, those few observations of his, as the native
production of his own Experience, being practised with care, the Vine-yards
in _England_ may be planted, govern'd and perpetuated with undoubted
success; and offering withall to furnish those, that have a desire to renew
this Culture, and to store their grounds with _Sets_ and _Plants_ of all
those sorts, which he recommends; he having a plentiful _stock_ of them
all.
* * * * *
Printed with Licence for _John Martyn_, and _James Allestry_, Printers to
the Royal Society. 1666.
{263}
* * * * *
_Num._ 16.
PHILOSOPHICAL
_TRANSACTIONS._
* * * * *
_Munday_, _August_ 6. 1666.
* * * * *
The Contents.
_An essay of Dr. _John Wallis_, exhibiting his _Hypothesis_ about the
_Flux and Reflux of the Sea_, taken from the consideration of the
_Common Center of Gravity of the Earth and Moon_; together with an
_Appendix_ of the same, containing an _Answer_ to some _Objections_,
made by severall Persons against that _Hypothesis_. Some Animadversions
of the same _Author_ upon Master _Hobs'_s late Book, _De Principiis &
Ratiocinatione Geometrarum_._
* * * * *
_An Essay of Dr. _John Wallis_, exhibiting his _Hypothesis_ about the _Flux
and Reflux of the Sea_._
How abstruse a subject in Philosophy, the _Flux and Reflux of the Sea_ hath
proved hitherto, and how much the same hath in all Ages perplexed the Minds
even of the best of _Naturalists_, when they have attempted to render an
Account of the Cause thereof, is needless here to represent. It may perhaps
be to more purpose, to take notice, that all the deficiencies, found in the
_Theories_ or _Hypotheses_, formerly invented for that End, have not been
able to deterre the Ingenious of _this_ Age from making farther search into
that Matter: Among whom that Eminent Mathematician Dr. _John Wallis_,
following his happy _Genius_ for advancing reall Philosophy, hath made it a
part of his later Inquiries and Studies, to contrive and deduce a certain
Hypothesis concerning that _Phaenomenon_, taken {264} from the Consideration
of the _Common Center of Gravity of the Earth and Moon_, This being by
several Learned Men lookt upon, as a very rational Notion, it was thought
fit to offer it by the Press to the Publick, that other Intelligent Persons
also might the more conveniently and at their leisure examine the
_Conjecture_ (the Author, such is his Modesty, presenting it no otherwise)
and thereupon give in their sense, and what Difficulties may occur to them
about it, that so it may be either confirm'd or laid aside accordingly; As
the _Proposer_ himself expressly desires in the Discourse, we now, without
any more _Preamble_, are going to subjoyn, as it was by him addressed, by
way of Letter, from _Oxford_ to Mr. _Boyle, April_ 25. 1666. and afterwards
communicated to the _R. Society_, as follows:
You were earnest with me, when you last went from hence, that I would put
in writing somewhat of that, which at divers times, these three or four
years last past, I have been discoursing with your self and others
concerning the _Common Center of Gravity of the Earth and Moon_, in order
to salving the _Phaenomena_ as well of the _Seas Ebbing and Flowing_; as of
some perplexities in _Astronomical Observations_ of the _Places_ of the
Celestial Bodies.
How much the World, and the great Bodies therein, are manag'd according to
the _Laws of Motion_, and _Statick Principles_, and with how much more of
clearness and satisfaction, many of the more abstruse _Phaenomena_ have been
salved on such Principles, within this last Century of years, than formerly
they had been; I need not discourse to you, who are well versed in it. For,
since that _Galilaeo_ and (after him) _Torricellio_, and others, have
applied _Mechanick_ Principles to the salving of _Philosophical_
Difficulties; _Natural Philosophy_ is well known to have been rendered more
intelligible, and to have made a much greater progress in less than an
hundred years, than before for many ages.
The _Seas Ebbing and Flowing_, hath so great a connexion with the _Moons_
motion, that in a manner all Philosophers (whatever other Causes they have
joyned with it), have attributed much of its cause to the _Moon_, which
either by some _occult quality_, {265} or _particular influence_, which it
hath on moyst Bodies, or by some _Magnetick vertue_, drawing the water
towards it, (which should therefore make the Water there _highest_, where
the Moon is _vertical_) or by its gravity and pressure downwards upon the
Terraqueous Globe (which would make it _lowest_ where the Moon is
_vertical_) or by whatever other means (according to the several
Conjectures of inquisitive persons,) hath so great an influence on, or at
least a connexion with, the Sea's Flux and Reflux, that it would seem very
unreasonable, to seclude the consideration of the Moons motion from that of
the Sea: The _Periods of Tides_ (to say nothing of the greatness of them
near the New moon and Full moon) so constantly waiting on the Moon's
motion, that it may be well presumed, that either the one is governed by
the other, or at least both from some common cause.
But the first that I know of, who took in the consideration of the
_Earth's_ motion, (_Diurnal_ and _Annual_) was _Galilaeo_; who in his
_Systeme of the World_, hath a particular discourse on this subject: Which,
from the first time I ever read it, seemed to me so very rational, that I
could never be of other opinion, but that the true Account of this great
_Phaenomenon_ was to be referred to the Earths motion, as the _Principal_
cause of it: Yet that of the Moon (for the reasons above mentioned) not to
be excluded, as to the determining the _Periods of Tides_, and other
circumstances concerning them. And though it be manifest enough, that
_Galilaeo_, as to some particulars, was mistaken in the account which there
he gives of it; yet that may be very well allowed, without any blemish to
so deserving a person, or prejudice to the _main Hypothesis_: For that
Discourse is to be looked upon onely as an _Essay_ of the _general
Hypothesis_; which as to _particulars_ was to afterwards adjusted, from a
good _General History of Tides_; which it's manifest enough that he had
not; and which is in a great measure yet wanting. For were the matter of
Fact well agreed on, it is not likely, that several Hypotheses should so
far differ, as that one should make the Water _then_ and _there_ at the
Highest, _where_ and _when_ the other makes it at the Lowest; as when the
Moon is Vertical to the place. {266}
And what I say of _Galilaeo_, I must in like manner desire to be understood
of what I am now ready to say to you. For I do not profess to be so well
skilled in the History of Tides, as that I will undertake presently to
accommodate my _general Hypothesis_ to the _particular cases_; or that I
will indeed undertake for the certainty of it, but onely as an _Essay_
propose it to further consideration; to stand or fall, as it shall be found
to answer matter of Fact. And truly had not your importunity (which is to
me a great Command) required me to do it, I should not so easily have drawn
up any thing about it, till I had first satisfied my selfe, how well the
Hypothesis would answer Observation: Having for divers years neglected to
do it, waiting a time when I might be at leisure throughly to prosecute
this design.
But there be two reasons, by which you have prevailed with me, at least to
do something. _First_, because it is the common Fate of the _English_, that
out of a modesty, they forbear to publish their Discoveries, till
prosecuted to some good degree of certainty and perfection; yet are not so
wary, but that they discourse of them freely enough to one another, and
even to Strangers upon occasion; whereby others, who are more hasty and
venturous, comming to hear of the notion, presently publish something of
it, and would be reputed thereupon, to be the first Inventers thereof:
though even that little, which they can then say of it, be perhaps much
less, and more imperfect, than what the true Authors could have published
long before, and what they had really made known (publikely enough, though
not in print) to many others. As is well known amongst us as to the
business of the _Lymphatick Vessels_ in _Anatomy_; the _Injection of
Liquors into the veins of Living animals_; the _Exhibiting of a straight
line equal to a crooked_; the _spot in Jupiter_, whence his motion about
his own Axis may be demonstrated; and many other the like considerable
Inventions.
The _other_ Reason (which, with me, is more really of weight, though even
the former be not cotemptible) is, because, as I have been already for at
least three or four years last past diverted from prosecuting the inquiry
or perfecting the Hypothesis, as I had thoughts to do; so I do not know,
but like Emergencies may divert me longer; and whether I shall ever so
{267} do it, as to bring it to perfection, I cannot determine. And
therefore, if as to my self any thing should _humanitus accidere_; yet
possibly the notion may prove worth the preserving to be prosecuted by
others, if I do it not. And therefore I shall, at least to your self, give
some general account of my present imperfect and undigested thoughts.
I consider therefore, that in the Tides, or the Flux and Reflux of the Sea,
besides extraordinary Extravagancies or Irregularities, whence great
Inundations or strangly high Tides do follow, (which yet perhaps may prove
not to be so meerly accidental as they have been thought to be, but might
from the regular Laws of Motion, if well considered, be both well accounted
for and even foretold;) There are these _three_ notorious Observations made
of the Reciprocation of Tides. _First_, the _Diurnal_ Reciprocation;
whereby twice in somewhat more than 24. hours, we have a Floud and an Ebbe;
or a High-water and Low-water. _Secondly_, the _Menstrual_; whereby in one
_Synodical_ period of the Moon, suppose from Full-moon to Full-moon, the
Time of those Diurnal Vicissitudes doth move round through the whole
compass of the [Greek: Nuchthemeron], or Natural day of twenty four hours:
As for instance, if at the Full-moon the full Sea be at such or such a
place just at Noon, it shall be the next day (at the same place) somewhat
before One of the clock; the day following, between One and Two; and so
onward, till at the New moon it shall be at midnight; (the other Tide,
which in the Full moon was at midnight, now at the New-moon coming to be at
noon;) And so forward till at the next Full-moon, the Full sea shall (at
the same place) come to be at Noon again: Again, That of the Spring-tides
and Neap-tides (as they are called;) about the Full-moon and New-moon the
Tides are at the Highest, at the Quadratures the Tides are at the Lowest:
And at the times intermediate, proportionably. _Thirdly_, the _Annual_;
whereby it is observed, that at sometimes of the year, the Spring-tides are
yet much higher than the Spring-tides at other times of the year: Which
Times are usually taken to be at the Spring and Autumne; or the two
AEquinoxes; but I have reason to believe (as well from my own Observations,
for many years, as of others who have been {268} much concerned to heed it,
whereof more will be said by and by;) that we should rather assign the
beginnings of _February_ and _November_, than the two _AEquinoxes_.
Now in order to the giving account of these three Periods, according to the
_Laws of Motion_ and _Mechanick Principles_; We shall _first_ take for
granted, what is now adayes pretty commonly entertained by those, who treat
of such matters; _That a Body in motion is apt to continue its motion, and
that in the same degree of celerity, unless hindred by some contrary
Impediment_; (like as a Body at rest, to continue so, unless by some
sufficient mover, put into motion:) And accordingly (which daily experience
testifies) if on a Board or Table, some loose incumbent weight, be for some
time moved, & have thereby contracted an _Impetus_ to motion at such a
rate; if that Board or Table chance by some external obstacle, or
otherwise, to be stopped or considerably retarded in its motion, the
incumbent loose Body will shoot forward upon it: And contrarywise, in case
that Board or Table chance to be accelerated or put forward with a
considerably greater speed than before, the loose incumbent Body, (not
having yet obtained an equal _Impetus_ with it) will be left behind, or
seem to fly backward upon it. Or, (which is _Galilaeo_'s instance,) if a
broad Vessel of Water, for some time evenly carried forward with the water
in it, chance to meet with a stop, or to slack its motion, the Water will
dash forward and rise higher at the fore part of the Vessel: And,
contrarywise, if the Vessel be suddenly put forward faster than before; the
Water will dash backwards, and rise at the hinder part of the Vessel. So
that an Acceleration or Retardation of the Vessel, which carries it, will
cause a rising of the Water in one part, and a falling in another: (which
yet, by its own weight, will again be reduced to a Level as it was before.)
And consequently, supposing the Sea to be but as a loose Body, carried
about with the Earth, but not so united with it, as necessarily to receive
the same degree of _Impetus_ with it, as its fixed parts do: The
acceleration or retardation in the motion of this or that part of the
Earth, will cause (more or less, according to the proportion of it) such a
dashing of the Water, or rising at one part, with a Falling at another, as
is that, which we call the Flux and Reflux of the Sea. {269}
[Illustration]
Now this premised, We are next, with him, to suppose the Earth carried
about with a double motion; The one _Annual_, as (_Fig._ 1.) in B E C the
great Orb, in which the Center of the Earth B, is supposed to move about
the Sun A.
The other _Diurnal_, whereby the whole moves upon its own _Axis_, and each
point in its surface describes a Circle, as D E F G.
It is then manifest, that if we suppose, that the Earth moved but by any
one of these motions, and that regularly, (with an equal swiftness;) the
Water, having once attained an equal _Impetus_ thereunto, would still hold
equal pace with it; there being no occasion, from the Quickening or
Slackening of the Earths motion, (in that part where the Water lyeth) for
the Water thereon either to be cast Forward or fall Backward; and thereby
to accumulate on the other parts of the Water: But the true motion of each
part of the Earths surface being compounded of those two motions, the
_Annual_ and _Diurnal_; (the _Annual_ in B E C being, as _Galilaeo_ there
supposeth, about three times as fast as a _diurnal_ motion in a great
Circle, as D E F;) while a Point in the Earths surface moves about its
Center B. from G. to D. and E. and at the same time, its Center B. be
carried forwards to C; the true motion of that Point forwards, is made up
of both those motions; to wit, of B to C, and of G to E; but while G moves
by D to E, E moves backward by F to G, contrary to the motion of B to C; so
that the true motion of E, is but the difference of B C, and E G: (for,
beside the motion of B above the Center; G. is also put forward as much as
from G to E; and E put backward as much as from E to G:) so that the
_Diurnal_ motion, in that part of the Earth, which is next the Sun, as E F
G, doth abate the progress of the _Annual_, (and most of all at F;) and in
the other part, which is from the Sun, as G D E, it doth increase it, (and
most of all at D.) that is, in the day time there is abated, in the night
time is added to the _Annual_ motion, about as much as is G E, the Earths
_Diameter_. Which would afford us a Cause of two Tides in twenty four
hours; the One upon the greatest Acceleration of motion, the Other upon its
greatest Retardation.
And thus far _Galilaeo_'s Discourse holds well enough; But then {270} in
this it comes short; that as it gives an Account of two Tides; so those two
Tides are alwayes to be at F and D; that is, at _Noon_ and _Midnight_;
whereas Experience tells us, that the Time of Tides, moves in a _moneths
space_ through all the 24. hours. Of which he gives us no account. For
though he do take notice of a Menstrual Period; yet he doth it onely as to
the _Quantity_ of the Tides; greater or less; not as to the _Time_ of the
_Tides_, sooner or later.
[Sidenote: * _Vid. Riccioli Almagest. novum_, Tom. 1, lib. 4. cap. 10. n.
111. pag. 216. 2.]
To help this, there is one (_Vid.* Jo. Baptista Balianus_) who makes the
_Earth_ to be but a _secondary_ Planet; and to move, not directly about the
Sun, but about the Moon, the Moon meanwhile moving about the Sun; in like
manner as we suppose the Earth to move about the Sun, and the Moon about
it.
But this, though it might furnish us with the foundation of a _Menstrual_
Period of Accelerations and Retardations in the compound motion of several
parts of the Earths surface; yet I am not at all inclined to admit this as
a _true Hypothesis_, for divers Reasons, which if not demonstrative, are
yet so consonant to the general Systeme of the World, as that we have no
good ground to disbelieve them. For 1. The Earth being undeniably the
greater Body of the two (whereof there is no doubt to be made) it cannot be
thought probable, that this should be carried about by the Moon, lesser
than it self: The contrary being seen, not onely in the _Sun_, which is
bigger than any of the Planets, which it carryes about; but in _Jupiter_,
bigger than any of his _Satellites_; and _Saturne_, bigger than his. 2. As
the _Sun_ by it's motion about it's own Axis, is with good reason judged to
be the _Physical_ cause of the _Primary_ Planets moving about it; So there
is the like reason to believe, that _Jupiter_ and _Saturne_ moving about
their Axes, are the Physical cause of their _Satellites_ moving about them,
which motion of _Jupiter_ hath been of late discover'd, by the help of a
_fixed_ Spot discern'd in him; and we have reason to believe the like of
_Saturne:_ Whether _Venus_ and _Mercury_ (about whom no _Satellites_ have
been yet observed) be likewise so moved; we have not yet the like ground to
determine: But we have of _Mars_; from {271} the Observations of Mr. _Hook_
made in _February_ and _March_ last, and by him communicated to the _Royal
Society_, and since Printed in the _Transactions_, published _Apr._ 2.
1666. consonant to the like observations of _Jupiter_, made by him in
_May._ 1664, and since communicated to the same _Society_; and then
published in the _Transactions_, of _March._ 6. then next following. Now
that the Earth hath such a motion about its own _Axis_ (whereby it might be
fitted to carry about the Moon) is evident by its _Diurnal_ motion. And it
seems as evident that the Moon hath not; because of the same side of the
Moon alwaies turned towards us; which could not be, if the Moon carried the
Earth about: Unlesse we should say, that it carries about the Earth in just
the same Period, in which it turnes upon its own Axis: Which is contrary to
that of the Sun carrying about the Planets: the shortest of whose Periods,
is yet longer than that of the Suns moving about its own Axis. And the like
of _Jupiter_, shorter than the Period of any of his _Satellites_; if at
least the Period of his conversion about his Axis, lately said to be
observed, prove true. (Of _Saturn_ we have not yet any Period assigned; but
it's likely to be shorter, than that of his _Satelles_.) And therefore we
have reason to believe, not that by the Moons motion about its Axis the
Earth should be carried by a contemporary Period (whereby the same face of
the Moon should be ever towards us;) but that by the Earths revolution
about its Axis in 24. hours, the Moon should be carried about it in about
29. dayes, without any motion on its own Axis: And accordingly, that the
_Secondary_ Planets about _Jupiter_ and _Saturn_, are not (like their
_Principals_) turned about their own Axis. And therefore I am not at all
inclined to believe, that the _Menstrual_ Period of the Tides with us, is
to be salved by such an Hypothesis.
In stead of this, that _Surmise_ of mine, (for I dare not yet, with
confidence give it any better name,) of what I have spoken to you
heretofore, (and which hath occasioned this present account which I am now
giving you,) is to this purpose.
The Earth and Moon being known to be Bodies of so great connexion (whether
by any Magnetick, or what other Tye, I will not determine; nor need I, as
to this purpose;) as that {272} the motion of the one follows that of the
other; (The Moon observing the Earth as the Center of its _periodick_
motion:) may well enough be looked upon as _one Body_, or rather _one
Aggregate of Bodies_, which have _one common center of Gravity_; which
Center (according to the known Laws of _Staticks_) is in a streight Line
connecting their respective Centers, so divided as that its parts be in
reciprocal proportion to the Gravities of the two Bodies. As for Example;
Suppose the Magnitude (and therefore probably, the Gravity) of the Moon to
be about an _One and fourtieth part_ of that of the Earth; (and thereabouts
_Hevelius_ in his _Selenography_ page 203. doth out of _Tycho_, estimate
the proportion; and an exact certainty is not necessary to our present
businesse.) And the distance of the Moons Center from the Center of the
Earth, to be about _fifty six Semidiameters_ of the Earth, (as thereabouts
he doth there estimate it, in its middle distance; and we need not be now
very accurate in determining the numbers; wherein Astronomers are not yet
very well agreed.) The distance of the Common Center of Gravity of the two
Bodies, will be from that of the Earth, about a two and fourtieth part of
fifty six Semidiameters; that is, about 56/42 or 4/3 of a Semidiameter;
that is about 1/3 of a Semidiameter of the Earth, above its surface, in the
Air, directly between the Earth and Moon.
Now supposing the Earth and Moon, joyntly as one Body, carried about by the
Sun in the great Orb of the _Annual_ motion; this motion is to be
estimated, (according to the Laws of _Staticks_, in other cases,) by the
motion of the common Center of Gravity of both Bodies. For we use in
_Staticks_, to estimate a Body, or Aggregate of Bodies, to be moved
upwards, downwards, or otherwise, so much as its Common Center of Gravity
is so moved, howsoever the parts may change places amongst themselves.
And accordingly, the Line of the _Annual_ motion, (whether _Circular_ or
_Elliptical_; of which I am not here to dispute,) will be described, not by
the Center of the Earth (as we commonly estimate it, making the Earth a
Primary and the Moon a Secondary Planet,) nor by the Center of the Moon,
(as they would do, who make the Moon the Primary and the Earth a {273}
Secondary Planet, against which we were before disputing:) But by the
_Common Center of Gravity of the Bodies, Earth and Moon_, as one Aggregate.
[Sidenote: See Fig. 2. and 3.]
Now supposing A B C D E to be a part of the great Orb of the _Annual_
motion, described by the Common Center of Gravity, in so long time as from
a _Full-Moon_ at A to the next _New-Moon_ at E; (which, though an Arch of a
_Circle_ or _Ellipse_, whose Center we suppose at a due distance below it;
yet being put about 1/25 of the whole, may well enough be here represented
by a streight Line:) the Center of the Earth at T, and that of the Moon at
L, must each of them (supposing their common Center of Gravity to keep the
Line A E) be supposed to describe a _Periphery_ about that Common Center,
as the Moon describes her Line of _Menstrual_ motion (Of which I have (in
the _Scheme_) onely drawn that of the _Earth_; as being sufficient to our
present purpose; parallel to which, if need be, we may suppose one
described by the Moon; whose distance is also to be supposed much greater
from T than in the _figure_ is expressed, or was necessary to expresse.)
And in like manner E F G H I, from that _New moon_ at E, to the next
_Full-moon_ at I.
[Illustration]
From A to E (from Full moon to New moon,) T moves (in its own _Epicycle_)
upwards from the Sun: And from E to I, (from New moon to Full moon) it
moves downwards, toward the Sun. Again, from C to G, (from last quarter to
the following first quarter,) it moves _forwards according_ to the _Annual_
motion; But from G forward to C, (from the first Quarter to the ensuing
last Quarter,) it moves _contrary_ to the _Annual_ motion.
It is manifest therefore, according to this Hypothesis, that from Last
quarter to First quarter (from C to G, while T is above the Line of the
_Annual_ motion) its _Menstrual_ motion in its Epicycle _adds_ somewhat of
Acceleration to the _Annual_ motion, and most of all at E, the New-moon:
And from the first to the last quarter (from G forward to C, while T is
below the Line of the _Annual_ motion,) it _abates_ of the _Annual_ motion;
and most of all at I, or A the Full-moon.
So that in pursuance of _Galilaeo's_ Notion, the _Menstrual_ {274} adding to
or detracting from the _Annual_ motion, should either leave behinde, or
cast forward, the loose waters incumbent on the Earth, (and thereby cause a
Tide, or accumulation of Waters) and most of all at the Full Moon and
New-moon, where those Accelerations or Retardations are greatest.
Now this _Menstrual_ motion, if nothing else were superadded to the
_Annual_, would give us two Tides in a moneth, and no more; (the one upon
the Acceleration, the other on the Retardation;) at New moon and Full-moon;
and two Ebbs, at the two Quarters; and in the Intervals, Rising and Falling
water.
But the _Diurnal_ motion superadded, doth the same to this _Menstrual_,
which _Galilaeo_ supposeth it to do to the _Annual_; that is, doth _Add_ to,
or _Subtract_ from, the _Menstrual_ Acceleration or Retardation; and so
gives us Tide upon Tide.
[Illustration]
For in whatsoever part of its Epicycle, we suppose T to be; yet because,
while by its _Menstrual_ motion the Center moves in the Circle L T N; each
point in its surface, by its diurnal motion moves in the Circle L M N:
whatever effect (accelerative or tardative) the _Menstrual_ would give,
that effect by the _Diurnal_ is increased in the parts L M N (or rather l M
n. the Semicircle) and most of all at M: but diminished in the parts N O L
(or rather n O l) and most of all at O. So that at M, and O, (that is when
the Moon is in the _Meridian_ below or above the _Horizon_,) we are to have
the Diurnal Tide or High-water, occasioned by the greatest Acceleration or
Retardation, which the _Diurnal_ Arch gives to that of the _Menstrual_:
which seems to be the true cause of the _Daily Tides_. And withall gives an
account, not onely why it should be _every_ day; but like wise, why at
_such a time_ of the day; and why this time should in a moneth run through
the whole 24 hours; _viz._ because the Moons coming to the _Meridian_ above
and below the _Horizon_, (or as the Seamen call it, the _Moons Southing_,
and _Northing_,) doth so: As likewise of the _Spring tides_ and
_Neap-tides_. For, when it so happens, that the _Menstrual_ and _Diurnal_
Accelerations or Retardations, be coincident, (as at New moons and
Full-moons they are,) the effect must needs be the greater. And although
(which is not to be dissembled) this happen {275} but to one of the two
Tides; that is, the Night-tide at the New-moon (when both motions do most
of all Accelerate,) and the Day-tide at Full-moon (when both do most Retard
the _Annual_ motion;) Yet, this tide being thus raised by two concurrent
causes; though the next Tide have not the same cause also, the _Impetus_
contracted will have influence upon the next Tide; Upon a like reason, as a
_Pendulum_ let fall from a higher Arch, will (though there be no new cause
to occasion it) make the Vibration on the other side (beyond the
Perpendicular) to be also greater: Or, of water in a broad Vessel, if it be
so jogged, as to be cast forward to a good height above its Levell, will
upon its recoyling, by its own gravity, (without any additional cause)
mount so much the higher on the hinder part.
But here also we are to take notice, that though all parts of the Earth by
its _Diurnal_ motion do turn about its Axis, and describe _parallel_
Circles; yet not _equal_ Circles; but _greater_ neer the _AEquinoctial_, and
_lesser_ near the _Poles_, which may be a cause why the Tides in some parts
may be much greater than in others. But this belongs to the _particular_
considerations, (of which we are not now giving an Account:) not to the
_general_ Hypothesis.
Having thus endeavoured to give an account of the _Diurnal_ and _Menstrual_
Periods of Tides; It remains that I endeavour the like as to the _Annual_.
Of which there is, at least, thus much agreed; That, at some times of the
year, the Tides are noted to be much higher, than at other times.
But here I have a double task; _First_, to rectify the Observation; and
_then_, to give an account of it.
As to the _First_; It having been observed (grosly) that those high Tides
have used to happen about the _Spring_ and _Autumn_; it hath been generally
taken for granted (without any more nice observation) that the _two
AEquinoxes_ are the proper times, to which these _Annual high Tides_ are to
be referred; And such causes sought for, as might best sute with such a
Supposition.
But it is now, the best part of twenty years, since I have had frequent
occasions to converse with some Inhabitants of _Rumney-marsh_ in _Kent_;
where the Sea being kept out with great Earthen walls, that it do not at
high water overflow the Levell; {276} and the Inhabitants livelyhood
depending most on grazing, or feeding Sheep; they are (as you may believe
they have reason to be) very vigilant and observant, at what times they are
most in danger of having their Lands drowned. And I find them generally
agreed, by their constant Observations, (and Experience dearly bought) that
their times of danger are about the beginning of _February_ and of
_November_; that is, at those Spring Tides which happen near those times;
to which they give the names of _Candlemass-stream_ and
_Allhallond-stream_; And if they scape those Spring-tides, they apprehend
themselves out of Danger for the rest of the year. And as for _March_ and
_September_ (the two _AEquinoxes_) they are as little solicitous of them, as
of any other part of the year.
This, I confess, I much wondred at, when I first heard it; and suspected it
to be but a mistake of him, that first told me, though he were indeed a
person not likely so to be mistaken, in a thing wherein he was so much
concerned: But I soon found, that it was not onely his, but a general
observation of others too; both there, and elsewhere along the Sea coast.
And though they did not pretend to know any reason of it, (nor so much as
to enquire after it;) Yet none made doubt of it; but would rather laugh at
any that should talk of _March_ and _September_, as being the dangerous
times. And since that time, I have my self very frequently observed (both
at _London_ and elsewhere, as I have had occasion), that in those months of
_February_ and _November,_ (especially _November_), the Tides have run much
higher, than at other times: Though I confess, I have not been so diligent
to set down those Observations, as I should have done. Yet this I do
particularly very well remember, that in _November_ 1660. (the same year
that his Majesty returned) having occasion to go by Coach from the _Strand_
to _Westminster_, I found the Water so high in the middle of _King-street_,
that it came up, not onely to the Boots, but into the Body of the Coach;
and the _Pallace-yard_ (all save a little place near the _West-End_)
overflow'd; as likewise the Market-place; and many other places; and their
Cellars generally filled up with Water. And in _November_ last, 1665. it
may yet be very well remembred, what very high Tides there were, not onely
on the Coasts of _England_, (where much hurt was {277} done by it) but much
more, in _Holland_, where by reason of those Inundations, many Villages and
Towns were overflow'd. And though I cannot so particularly name other
years, yet I can very safely say, that I very often observed Tides
strangely high about those times of the year.
This Observation did for divers years cause me much to wonder, not only
because it is so contrary to the received opinion of the two _AEquinoxes_;
but because I could not think of any thing signal at those times of the
year: as being neither the two _AEquinoxes_, nor the two _Solstices_, nor
the Sun's _Apogaeum_ and _Perigaeum_: (or Earths _Aphelium_ and
_Perihelium_;) nor indeed, at contrary times of the year, which at least,
would seem to be expected. From _Alhollandtide_ to _Candlemass_ being but
three months; and from thence to _Alhollandtide_ again nine months.
At length it came into my mind, about four years since, that though there
do not about these times happen any _single_ signal Accident, which might
cast it on these times, yet there is a _compound of two_ that may do it;
Which is the _Inequality_ of the _Natural day_ (I mean that of 24. hours,
from noon to noon) arising at least from a double cause; either of which
singly would cast it upon other times, but both joyntly on those.
It's commonly thought, how unequal soever the length be of the _Artificial_
dayes as contradistinguished to nights, yet that the _Natural_ Days,
reckoning from noon to noon, are all _equal_: But _Astronomers_ know well,
that even these dayes are _unequal_.
For, this _Natural_ Day is measured _not onely_ by one intire conversion of
the _AEquinoctial_, or 24. _AEquinoctial_ hours, (which is indeed taken to be
performed in equal times,) _but_ increases by so much, as answers to that
part of the _Sun's_ (or _Earths_,) Annual motion as is performed in that
time. For, when that part of the _AEquinoctial_, which (with the _Sun_) was
the _Meridian_ yesterday at noon, is come thither again to day, it is not
yet _Noon_ (because the Sun is not now at the place where yesterday he was,
but is gone forward about one degree, more or less) but we must stay till
that place, where the _Sun_ now is, comes to the _Meridian_ before it be
now _Noon_.
Now this Additament (above the 24 _AEquinoctial_ hours, or intire conversion
of the _AEquinoctial_) is upon a double account {278} unequal. _First_,
because the Sun, by reason of its _Apogaeum_ and _Perigaeum_, doth not at all
times of the year dispatch in one day an equal Arch of the _Ecliptick_; but
greater Arches neer the _Perigaeum_, which is about the middle of
_December_; and lesser neer the _Apogaeum_, which is about the middle of
_June_: As will appear sufficiently by the _Tables_ of the Sun's Annual
motion. _Secondly_, though the Sun should in the _Ecliptick_ move alwaies
at the same rate; yet equal Arches of the _Ecliptick_ do not in all parts
of the _Zodiack_ answer to equal Arches of the _AEquinoctial_, by which we
are to estimate time: Because some parts of it, as about the two
_Solsticial_ Points, lie nearer to a _parallel_ position to the
_AEquinoctial_, than others, as those about the two _AEquinoctial_ points,
where the _Ecliptick_ and _AEquinoctial_ do intersect; whereupon an Arch of
the _Ecliptick_, neer the _Solsticial_ points answers to a greater Arch of
the _AEquinoctial_, than an Arch equal thereunto neer the _AEquinoctial_
points: As doth sufficiently appear by the _Tables_ of the Suns _right
Ascension_.
According to the _first_ of these causes, we should have the longest
_natural_ daies in _December_, and the shortest in _June_, which if it did
operate alone, would give us at those times two _Annual_ High-waters.
According to the _second_ cause, if operating singly, we should have the
longest daies at the two Solstices in _June_ and _December_, and the two
shortest at the _AEquinoxes_ in _March_ and _September_; which would at
those times give occasion of four _Annual_ High-waters.
But the true _Inequality_ of the Natural Days, arising from a _Complication
of those two causes_, sometimes crossing and sometimes promoting each each
other: though we should find some increases or decreases of the _Natural_
daies at all those seasons answerable to the respective causes (and perhaps
of Tides proportionably thereunto:) yet the longest and shortest _natural
daies_ absolutely of the whole year (arising from this complication of
Causes) are about those times of _Allhallontide_ and _Candlemas_; (or not
far from them) about which those _Annual_ High-tides are found to be: As
will appear by the _Tables of AEquation_ of _Natural_ daies. And therefore I
think, we may with very good reason cast this _Annual_ Period upon that
cause, or rather {279} complication of causes. For (as we before shewed in
the _Menstrual_ and _Diurnal_) there will, by this inequality of Natural
daies, arise a _Physical_ Acceleration and Retardation of the Earths _Mean_
motion, and accordingly a casting of the Waters backward or forward; either
of which, will cause an Accumulation or High-water.
'Tis true, that these longest and shortest daies, do (according to the
_Tables_, some at least) fall rather before, than after _Alhallontide_ and
_Candlemas_ (to wit the ends of _October_ and _January_;) but so do also
(sometimes) those high Tydes: And it is not yet so well agreed amongst
_Astronomers_, what are all the Causes (and in what degrees) of the
Inequality of Natural daies; but that there be diversities among them,
about the true time: And whether the introducing of this New Motion of the
Earth in its _Epicycle_ about this Common Center of _Gravity_, ought not
therein also to be accounted for, I will not now determine: Having already
said enough, if not too much, for the explaining of this general
Hypothesis, leaving the particularities of it to be adjusted according to
the true measures of the motions; if the General Hypothesis be found fit to
be admitted.
Yet this I must add, (that I be not mistaken) that whereas I cast the time
of the daily Tydes to be at all places, when the Moon is there in the
_Meridian_; it must be understood of _open_ Seas, where the water hath such
free scope for its motions, as if the whole Globe of Earth were equally
covered with water: Well knowing, that in _Bayes_ and _In land-Channels_,
the position of the Banks and other like causes must needs make the times
to be much different from what we suppose in the open Seas: And likewise,
that even in the Open Seas, _Islands_, and _Currents_, _Gulfs_ and
_Shallows_, may have some influence, though not comparable to that of
_Bays_ and _Channels_. And moreover, though I think, that Seamen do
commonly reckon the time of High-water in the _Open Seas_, to be then, when
the Moon is there in the _Meridian_ (as this Hypothesis would cast it:) Yet
I do not take my self to be so well furnished with a _History of Tides_, as
to assure my self of it; much less to accommodate it to particular places
and cases.
Having thus dispatched the main of what I had to say {280} concerning the
Seas Ebbing and Flowing: Had I not been already too tedious, I should now
proceed to give a further reason, why I do introduce this consideration of
the _Common Center of Gravity_ in reference to _Astronomical Accounts_. For
indeed, that which may possibly seem at first to be an Objection _against_
it, is with me one reason _for_ it.
It may be thought perhaps, that if the Earth should thus describe an
_Epicycle_ about the Common Center of Gravity, it would (by this its change
of place) disturbe the _Caelestial_ motions; and make the _apparent_ places
of the Planets, especially some of them, different from what they would
otherwise be. For though so small a removal of the Earth, as the _Epicycle_
would cause (especially if its _Semidiameter_ should not be above 1-1/3 of
the Earths Semidiameter) would scarce be sensible (if at all) to the
remoter Planets; yet as to the nearer it might.
Now though what _Galilaeo_ answers to a like Objection in his _Hypothesis_;
(that its possible there may be some small difference, which _Astronomers_
have not yet been so accurate, as to observe) might here perhaps serve the
turn; Yet my answer is much otherwise; to wit, that such difference hath
been observed and hath very much puzzeled _Astronomers_ to give an account
of. About which you will find Mr. _Horrocks_ (in some of his Letters,
whereof I did formerly, upon the Command of the _Royal Society_, make an
_Extract_) was very much perplexed; and was fain, for want of other relief,
to have recourse to somewhat like _Keplers_ amicable _Fibres_, which did
according to the several positions of the Moon, accelerate or retard the
Moon's motion; which _amicable Fibres_ he had no affection to at all (as
there appears) if he could any other waies give account of those little
inequalities; and would much rather (I doubt not) have embraced this Notion
of the Common Center of Gravity, to salve the _Phaenomenon_, had it come to
his mind, or been suggested to him. And you find, that other _Astronomers_
have been seen to bring in (some upon one supposition, some upon another)
some kind of _Menstrual AEquation_, to solve the inequalities of the Moon's
motion, according to her _Synodical_ Revolution, or different Aspects (of
New-moon, Full Moon, &c.) beside what concerns her own _Periodical_ motion.
{281}
For which, this consideration of the _Common Center of Gravity of the Earth
and Moon_, is so proper a remedy (especially if it shall be found precisely
to answer those _Phaenomena_, which I have not Examined, but am very apt to
believe) that it is so far from being, with me, an Objection against it,
that it is one of the reasons, which make me inclinable to introduce it.
I must before I leave this, add one Consideration more, That if we shall
upon these Considerations think it reasonable, thus to consider the _Common
Center of Gravity of the Earth and Moon_; it may as well be thought
reasonable, that the like Consideration should be had of _Jupiter_ and his
four _Satellites_, which according to the Complication of their several
motions, will somewhat change the position of _Jupiter_, as to that _Common
center of Gravity_ of all these Bodies; which yet, because of their
smallness, may chance to be so little, as that, at this distance, the
change of his apparent place may not be discernable. And what is said of
_Jupiter_, is in the like manner to be understood of _Saturne_ and his
_Satelles_, discovered by _Hugenius_: For all these _Satellites_ are to
their _Principals_, as so many Moons to the Earth. And I do very well
remember, in the Letters forecited, Mr. _Horrocks_ expresseth some such
little inequalities in _Saturnes_ motion, of which he could not imagine
what account to give, as if (to use his Expression) this crabbed _Old
Saturn_ had despised his _Youth_. Which, for ought I know, might well
enough have been accounted for, if at that time the _Satelles_ of _Saturn_
had been discovered, and that Mr. _Horrocks_ had thought of such a notion
as the _Common Center of Gravity_ of _Saturn_ and his _Companion_, to be
considerable, as to the guiding of his motion.
You have now, in obedience to your Commands, an Account of my thoughts, as
to this matter, though yet immature and unpolished: What use you will
please to make of them, I shall leave to your prudence, &c.
* * * * *
_An _APPENDIX_, written by way of Letter to the _Publisher_; Being an
answer to some Objections, made by several Persons, to the precedent
Discourse._
I Received yours; and am very well contented, that _objections_ be made
against my _Hypothesis_ concerning _Tydes_: being {282} proposed but as a
conjecture to be examined; and, upon that Examination, rectified, if there
be occasion; or rejected, if it will not hold water.
1. To the first objection of those you mention; _That it appears not how
two Bodies, that have no tye, can have one common Center of Gravity:_ that
is (for so I understand the intendment of the objection) can act or be
acted in the same manner, as if they were connected: I shall onely answer,
that it is harder to shew _How_ they have, than _That_ they have it. That
the Load-stone and Iron have somewhat equivalent to a Tye; though we see it
not, yet by the effects we know. And it would be easy to shew, that two
Load-stones, at once applyed, in different positions, to the same Needle,
at some convenient distance, will draw it, not to point directly to either
of them, but to some point between both; which point is, as to those two,
the _common Center of Attraction;_ and it is the same, as if some _one_
Load-stone were in that point. Yet have these two Load stones no connection
or tye, though a _Common Center of Virtue_ according to which they joyntly
act. And as to the present case, _How_ the Earth and Moon are connected; I
will not now undertake to shew (nor is it necessary to my purpose;) but,
That there is somewhat, that doth connect them, (as much as what connects
the Load-stone, and the Iron, which it draws,) is past doubt to those, who
allow them to be carryed about by the Sun, as one Aggregate or Body, whose
parts keep a respective position to one another: Like as _Jupiter_ with his
_four Satellites_, and _Saturn_ with his _one_. Some Tye there is, that
makes those _Satellites_ attend their _Lords_, and move in a Body; though
we do not _See_ that Tye; nor _Hear_ the Words of Command. And so here.
2. To the second objection; _That, at Chatham and in the Thames, the Annual
Spring-tydes, happen about the AEquinoxes; not (as this Hypothesis doth
suppose elsewhere to have been observed) about the beginning of February
and November._ If their meaning be, that Annual High Tydes, do then happen,
and then onely: If this prove true, it will ease me of half my work. For it
is then easily answered, that it depends upon the _Obliquity of the
Zodiack_; the parts of the AEquinoctial answering to equal parts of the
{283} _Zodiack_, being neer the Solstitial points greatest, and near the
AEquinoctial points least of all. But beside this _Annual Vicissitude of the
AEquinoxes_, not to say, of the 4. Cardinal Points (which my Hypothesis doth
allow and assert;) I believe it will be found, that there is _another
Annual vicissitude_ answering to the Suns _Apogaeum_ and _Perigaeum_. And
that the greatest Tydes of all, will be found to be upon a result of these
two causes Cooperating: which (as doth the Inequality of Natural dayes,
depending on these same causes) will light nearer the times, I mention. To
what is said to be observed at _Chatham_ and in the _Thames_, contrary to
that I allege as observed in _Rumney marsh_: I must at present [Greek:
apechein], and refer to a _melius inquirendum_. If those who object this
contrary observation, shall, after this notice, find, upon new Observations
heedfully taken, that the _Spring-tydes_ in _February_ and _November_, are
not so high, as those in _March_ and _September_; I shall then think the
objection very considerable. But I do very well remember, that I have seen
in _November_, very high Tydes at _London_, as well as in _Rumney Marsh_.
And, the time is not yet so far past, but that it may be remembered (by
your self or others then in _London_) whether in _November_ last when the
Tydes were so high at _Dover_, at _Deal_, at _Margate_, and all along the
Coast from thence to _Rumney Marsh_, as to do in some of those places much
hurt, (and, in _Holland_, much more;) whether, I say, there were not also
at the same time, at _London_, (upon the _Thames_) very high Tydes. But a
good _Diary_ of the Height and time both of High-water, and Low-water, for
a year or two together, even at _Chatham_, or _Greenwich_; but rather at
some place in the _open_ Sea, or at the _Lands end_ in _Cornwal_, or on the
_West parts of Ireland_; or at St. _Hellens_, or the _Bermodas_, &c. would
do more to the resolving of this point, than any verbal discourse without
it.
3. To the third Objection, _That supposing the Earth and Moon to move about
a Common center of gravity; if that the highest Tydes be at the New-moon,
when the moon being nearest to the Sun, the Earth is farthest from it, and
its compound motion at the swiftest; and that the Tydes abate as the Earth
approacheth nearer; till it comes into the supposed Circle of her Annual
motion: It may be demanded, why do they not still abate as the Earth comes
yet nearer to the Sun; and the_ {284} _swiftnesse of its compound motion
still slackens? And so, why have we not Spring tides at the New Moon (when
the motion is swiftest) and Neap tides at Full Moon (when the motion is
slowest) but Spring tides at both?_ The answer (if observed) is already
given in my _Hypothesis_ it self. Because the effect is indifferently to
follow, either upon a suddain Acceleration, or a suddain Retardation. (Like
as a loose thing, lying on a moving body; if the body be thrust suddainly
forward, that loose thing is cast back, or rather left behind, not having
yet obtained an equal _impetus_ with that of the body, on which it lyes;
but if stopped, or notably retarded, that loose incumbent is thrown
forward, by its formerly contracted _impetus_ not yet qualified or
accomodated to the slowness of the Body, on which it lyes.) Now both of
these happening, the one at the New Moon, the other at the Full Moon, do
cause high Tides at both.
4. To the fourth Objection, _That the highest Tydes are not at all places,
about the New Moon and Full Moon; and particularly, that, in some places of
the East Indies, the Highest Tydes are at the Quadratures_: I must first
answer in _general_; That as to the particular varieties of Tydes in
several parts of the World, I cannot pretend to give a satisfactory
account, for want of a competent History of Tydes, &c. Because (as is
intimated in what I wrote in the _general_) the various positions of
Chanels, Bays, Promontories, Gulfs, Shallows, Currents, Trade-winds, &c.
must needs make an innumerable variety of Accidents in particular places,
of which no satisfactory account is to be given from the general
_Hypothesis_ (though never so true) without a due consideration of all
those. Which is a task too great for me to undertake, being so ill
furnished with materials for it. And then as to the particular instance of
some places in the _East Indies_, where the highest Tydes are at the
_Quadratures_: I suppose, it may be chiefly intended of those about
_Cambaia_, and _Pegu_. At which places, beside that they are situate at the
inmost parts of Vast Bayes, or Gulfs (as they are called) they have also
vast In-draughts of some hundred Miles within Land; which when the Tydes
are out, do lye (in a manner) quite dry: And may therefore very well be
supposed to participate the effect of the Menstrual Tydes many dayes after
the {285} cause of them happens in the open Sea, upon a like ground as in
Straights and narrow Channels the Diurnall Tydes happen some hours later
than in the Ocean. And a like account must be given of particular accidents
in other places, from the particular situation of those places, as _Bays_,
_Chanels_, _Currents_, &c.
5. To the 5. Objection, _That the Spring-Tydes happen not, with us, just at
the Full and Change, but two or three daies after_. I should with the more
confidence attempt an Answer, were I certain, whether it be so in the
_Open_ Seas, or onely in our Channels. For the Answers will not be the same
in both cases. If onely in our Channels, where the Tydes find a large
in-draught; but not in the Open Seas: we must seek the reason of it from
the particular position of these places. But if it be so generally in the
wide Open Seas: We must then seek a reason of it from the general
Hypothesis. And, till I know the matter of Fact, I know not well, which to
offer at; lest whilst I attempt to salve one, I should fall foul of the
other. I know that Marriners use to speak of Spring-Tydes at the New and
Full of the Moon; though I have still had a suspition that it might be some
daies after, as well in the open Seas, as in our narrower Channels; (and
therefore I have chosen to say, in my Papers, _About_ the New and Full,
rather than _At_ the New and Full; and even when I do say _At_, I intend it
in that laxer sense in which I suppose the Marriners are to be understood,
for _Neer_ that time:) Of which suspition you will find some intimations
even in my first Papers: But this though I can admit; yet, because I was
not sure of it, I durst not build upon it. The truth is, the Flux and
Reflux of water in a vessel, by reason of the jogging of it, though it
follow thereupon; yet is, for the most part, discernable some time after.
For there must, upon that jog, be some time for Motion, before the
Accumulation can have made a Tyde. And so I do not know but that we must
allow it in all the Periods. For as the _menstrual_ High Tyde, is not (at
least with us) till some Daies after the Full and Change; so is the
_Diurnal_ High water, about as many Hours, after the Moons comming to
South; (I mean, At Sea: for in Chanels it varies to all Hours, according as
they are neerer or further from the open Sea:) And the _Annual_ High-Tydes
of _November_ and _February_; somewhat later than {286} (what I conjecture
to be from the same causes) the greatest Inequalities of the natural Days,
happening in _January_ and _October_. But this though I can admit, yet
(till I am sure of the matter of Fact) I do not build upon. And since it
hath hitherto been the custome to speak with that laxness of expression;
assigning the times of New-moon, Full-moon, and Quadratures, with the Moons
comming to South, for, what is neer those times: I did not think myself
obliged in my conjectural Hypothesis (while it is yet but a _Candidate_) to
speak more nicely. If the Hypothesis for the maine of it be found Rational;
the Niceties of it are to be adjusted, in time, from particular
Observation.
Having thus given you some Answers to the Objections you signifie to have
been made by several persons to my Hypothesis, and that in the same order
your Paper presents them to me; I shall next give you some account of the
two _Books_, which you advised me to consult; so far as seems necessary to
this business; Which, upon your intimation, I have since perused, though
before I had not.
And first, as to that of _Isaac Vossius, De motu Marium & Ventorum_; Though
I do not concur with him in his Hypothesis; That all the _Great motions of
the Seas_, &c. should arise onely from _so small a warming of the water_ as
to raise it (where most of all) _not a Foot_ in perpendicular, (as in his
12_th_ Chapter.) Or that there is no other connexion between the Moons
motion, and the Tydes _menstrual_ period, than a _casual Synchronism_
(which seems to be the doctrine of his 16_th_ and 18_th_ Chapters;) Beside
many other things in his Philosophy, which I cannot allow: Yet I am well
enough pleased with what is Historical in it, of the matter of Fact:
Especially if I may be secure, that he is therein accurate and candid, not
wresting the _Phaenomena_ to his own purpose. But I find nothing in it,
which doth induce me to vary from my Hypothesis. For, granting his
Historicals to be all true; the account of the constant Current of the Sea
Westward, and of the constant Eastern Blasts, &c. within the _Tropicks_, is
much more plausibly, and (I suppose) truly rendered by _Galilaeo_ long
since, from the Earths _Diurnal_ motion: (which, neare the _AEquator_,
describing a greater Circle, than nearer the {287} _Poles_, makes the
Current to be there more conspicuous and swift, and consequently, the Eddy,
or recurrent motion, nearer the Poles, where this is, more remiss:) than
can easily be rendered by so small a Tumor, as he supposeth. Not to adde;
that his account of the Progressive motion, which he fansieth to follow
upon this Tumefaction, and by Acceleration to grow to so great a height
near the Shoar (as in Chap. 13. and 14.) is a Notion, which seems to me too
extravagant to be salved by any laws of _Staticks_. And that of the Moons
motion onely Synchronizing with the Tydes, casually, without any _Physical_
connexion; I can very hardly assent to. For it can hardly be imagined, that
any such constant _Synchronisme_ should be in Nature; but where, either the
one is the cause of the other, or both depend upon some _Common_ cause. And
where we see so fair a foundation for a _Physical_ connection. I am not
prone to ascribe it to an Independent Sychronism. In sum; His History doth
well enough agree with my Hypothesis; and I think, the Phaenomena are much
better salved by mine, than his.
And then as to _Gassendus_, in his discourse _De AEstu Maris_; I find him,
after the relating of many other Opinions concerning the Cause of it,
inclining to that of _Galilaeo_, ascribing it to the Acceleration &
Retardation of the Earths motion, compounded of the Annual and Diurnal; And
moreover attempting to give an account of the _Menstrual Periods_ from the
Earths carrying the Moon about it self, as _Jupiter_ doth his _Satellites_;
which together with them is carryed about by the _Sun_, as one Aggregate;
(and that the Earth with its Moon is to be supposed in like manner to be
carried about by the Sun, as one Aggregate, cannot be reasonably doubted,
by those who entertain the _Copernican Hypothesis_, and do allow the same
of _Jupiter_ and his _Satellites_.) But though he would thus have the Earth
and Moon looked upon as two parts of the same moved Aggregate, yet he doth
still suppose (as _Galilaeo_ had done before him) that the line of the Mean
Motion of this Aggregate (or, as he calls, _motus aequabilis et veluti
medius_) is described by the _Center_ of the _Earth_ (about which Center he
supposeth both its own revolution to be made, and an Epicycle described by
the Moons motion;) not by another Point, distinct from the Centers of both,
about which, as the {288} common Center of Gravity, as well that of the
Earth, as that of the Moon, are to describe several Epicycles. And, for
that Reason fails of giving any clear account of this _Menstrual_ Period.
(And in like manner, he proposeth the Consideration as well of the Earths
_Aphelium_ and _Perihelium_ as of the _AEquinoctial_ and _Solstitial_
Points, in order to the finding a Reason of the _Annual_ Vicissitudes; but
doth not fix upon any thing, in which himself can Acquiesce: And therefore
leaves it _in medio_ as he found it.)
It had been more agreeable to the Laws of _Staticks_, if he had, (as I do,)
so considered the _Earth_ and _Moon_ as two parts of the same movable, (not
so, as he doth, _aliam in Centro et sequentem praecise revolutionem axis,
aliam remotius ac velut in circumferentia_, but,) so, as to make neither of
them the Center, but both out of it, describing Epicycles about it: Like
as, when a long stick thrown in the Air, whose one end is heavyer than the
other, is whirled about, so as that the End, which did first fly foremost,
becomes hindmost; the proper line of motion of this whole Body is not that,
which is described by either End, but that, which is described by a middle
point between them; about which point each end, in whirling, describes an
Epicycle. And indeed, in the present case, it is not the Epicycle described
by the Moon, but that, described by the Earth, which gives the _Menstrual_
Vicissitudes of motion to the Water; which would, as to this, be the same,
if the Earth so move, whether there were any Moon to move or not; nor would
the Moons Motion, supposing the Earth to hold on its own course, any whit
concern the motion of the Water.
[Illustration]
But now, (after all our Physical, or Statical Considerations) the clearest
Evidence for this Hypothesis (if it can be had) will be from Celestial
Observations. As for instance; (see _Fig._ 5.) Supposing the Sun at S; the
Earths place in its Annual Orb at T; and _Mars_ (in opposition to the Sun,
or near it) at M: From whence _Mars_ should appear in the Zodiack at
[gamma], and will at Full moon be seen there to be; the Moon being at C and
the Earth at c; (and the like at the New-moon.) But if the Moon be in the
First quarter at A, and the Earth at a: _Mars_ will be seen, not at
[gamma], but at [alpha]; too slow: And when the Moon is at B, and the Earth
at b, _Mars_ will be seen at [beta]; yet too slow: till at the {289}
Full-moon, the Moon at C, the Earth at c, _Mars_ will be seen at [gamma],
its true place, as if the Earth were at T. But then, after the Full, the
Moon at D, the Earth at d; _Mars_ will be seen, not at [gamma], but at
[delta], too forward: and yet more, when the Moon (at the last Quarter) is
at E, the Earth at e, and _Mars_ seen at [epsilon]. If therefore _Mars_
(when in opposition to the Sun) be found (all other allowances being made)
somewhat too backward before the Full moon, and somewhat too forward after
the Full-moon, (and most of all, at the Quadratures:) it will be the best
confirmation of the Hypothesis. (The like may be fitted to _Mars_ in other
positions, _mutatis mutandis_; and so for the other Planets.)
But this proof, is of like nature as that of the Parallaxis of the Earths
Annual Orb to prove the Copernican Hypothesis. If it can be observed, it
proves the Affirmative; but if it cannot be observed, it doth not convince
the Negative, but only proves that the Semidiameter of the Earths Epicycle
is so small as not to make any discernable Parallax. And indeed, I doubt,
that will be the issue. For the Semidiameter of this Epicycle, being little
more than the Semidiameter of the Earth it self, or about 1-1/3 thereof (as
is conjectured, in the _Hypothesis_, from the Magnitudes and Distances of
the Earth and Moon compared;) and there having not as yet been observed any
discernable _Parallax_ of _Mars_, even in his neerest position to the
Earth; it is very suspicious, that here it may prove so too. And whether
any of the other Planets will be more favourable in this point, I cannot
say.
* * * * *
_ANIMADVERSIONS of Dr. _Wallis_, upon Mr. _Hobs_'s late Book, _De
Principiis & Ratiocinatione Geometrarum_._
These were communicated by way of Letter, written in _Oxford_, July 24.
1666. to an Acquaintance of the _Author_, as follows:
Since I saw you last, I have read over Mr. _Hobs_'s Book _Contra Geometras_
(or _De Principiis & Ratiocinatione Geometrarum_) which you then shewed me.
A New Book of _Old_ matter: Containing but a _Repetition_ of what he had
before told us, more than once; and which hath been Answered long agoe.
In which, though there be Faults enough to offer ample {290} matter for a
large Confutation; yet I am scarce inclined to believe, that any will
bestow so much pains upon it. For, if that be true, which (in his
_Preface_) he saith of himself, _Aut solus insanio Ego, aut solus non
insanio_: it would either be _Needless_, or _to no Purpose_. For, by his
own confession, _All others_, if they be not mad themselves, ought to think
_Him_ so: And therefore, as to _Them_ a Confutation would be _needless_;
who, its like, are well enough satisfied already: at least out of danger of
being seduced. And, as to himself, it would be _to no purpose_. For, if
_He_ be the Mad man, it is not to be hoped that he will be convinced by
Reason: Or, if _All We_ be so; we are in no capacity to attempt it.
But there is yet another Reason, why I think it not to need a Confutation.
Because what is in it, hath been sufficiently confuted already; (and, so
Effectually; as that he professeth himself not to Hope, that _This Age_ is
like to give sentence for him; what ever _Nondum imbuta Posteritas_ may
do.) Nor doth there appear any Reason, why he should again Repeat it,
unless he can hope, That, what was at first False, may by oft Repeating,
become True.
I shall therefore, instead of a large Answer, onely give you a brief
Account, _what is in it_; &, _where it hath been already Answered_.
The chief of what he hath to say, in his first 10 Chapters, against
_Euclids_ Definitions, amounts but to this, That he thinks, _Euclide_ ought
to have allowed his _Point_ some _Bigness_; his _Line_, some _Breadth_; and
his _Surface_, some _Thickness_.
But where in his _Dialogues_, pag. 151, 152. he solemnly undertakes to
Demonstrate it; (for it is there, his 41th _Proposition_:) his
Demonstration amounts to no more but this; That, _unless a Line be allowed
some Latitude; it is not possible that his Quadratures can be True_. For
finding himself reduced to these inconveniences; 1. That his _Geometrical
Constructions_, would not consist with _Arithmetical calculations_, nor
with what _Archimedes_ and others have long since demonstrated: 2. That the
_Arch_ of a Circle must be allowed to be sometimes _Shorter_ than its
_Chord_, and sometimes _longer_ than its _Tangent_: 3. That the same
Straight Line must be allowed, at one place onely to _Touch_, and at
another place to _Cut_ the same Circle: (with others of like nature;) He
findes it necessary, that these things may not seem Absurd, to allow his
_Lines_ some _Breadth_, (that so, as he speaks, _While a Straight Line with
its Out-side doth at one place {291} Touch the Circle, it may with its
In-side at another place Cut it_, &c.) But I shou'd sooner take this to be
a _Confutation of His Quadratures_, than a _demonstration of the Breadth of
a _(Mathematical)_ Line_. Of which, see my _Hobbius Heauton-timorumenus_,
from _pag._ 114. to p. 119.
And what he now Adds, being to this purpose; That though _Euclid_'s [Greek:
Semeion], which we translate, _a Point_, be not indeed _Nomen Quanti_; yet
cannot this be actually represented by any thing, but what will have some
Magnitude; nor can _a Painter_, no not _Apelles_ himself, draw a _Line_ so
small, but that it will have some Breadth; nor can _Thread_ be spun so
Fine, but that it will have some Bigness; (_pag._ 2, 3, 19, 21.) is nothing
to the Business; For _Euclide_ doth not speak either of such _Points_, or
of such _Lines_.
He should rather have considered of his own Expedient, _pag._ 11. That,
when one of his (_broad_) Lines, passing through one of his (_great_)
Points, is supposed to cut another Line proposed, into two equal parts; we
are to understand, the _Middle of the breadth_ of that Line, passing
through the _middle_ of that Point, to distinguish the Line given into two
equal parts. And he should then have considered further, that _Euclide_, by
a _Line_, means no more than what Mr. _Hobs_ would call _the middle of the
breadth_ of his; and _Euclide_'s _Point_, is but the _Middle_ of Mr.
_Hobs_'s. And then, for the same reason, that Mr. _Hobs_'s _Middle_ must be
said to have no _Magnitude_; (For else, not the _whole Middle_, but the
_Middle of the Middle_, will be _in the Middle_: And, the _Whole_ will not
be equal to its _Two Halves_; but Bigger than _Both_, by so much as the
_Middle_ comes to:) _Euclide_'s _Lines_ must as well be said to have no
Breadth; and his _Points_ no Bigness.
In like manner, When _Euclide_ and others do make the _Terme_ or _End_ of a
Line, a _Point_: If this _Point_ have _Parts_ or _Greatness_, then not the
_Point_, but the _Outer-Half_ of this Point ends the Line, (for, that the
_Inner-Half_ of that Point is not at the End, is manifest, because the
_Outer-Half_ is beyond it:) And again, if that _Outer Half_ have _Parts_
also; not this, but the _Outer_ part of it, and again the _Outer part_ of
that _Outer part_, (and so in _infinitum_.) So that, as long as _Any thing
of Line_ remains, we are not yet at the _End_: And consequently, if we must
have passed the _whole Length_, before we be at the _End_; then that _End_
(or _Punctum terminans_) has _nothing of Length_; (for, when the _whole
Length_ is past, there is nothing of it left.) And if Mr. _Hobs_ tells us
(as _pag._ 3.) that this {292} _End_ is not _Punctum_, but only _Signum_
(which he does allow _non esse nomen Quanti_) even _this_ will serve our
turn well enough. _Euclid_'s [Greek: Semeion], which some Interpreters
render by _Signum_, others have thought fit (with _Tully_) to call
_Punctum_: But if Mr. _Hobs_ like not that name, we will not contend about
it. Let it be _Punctum_, or let it be _Signum_ (or, if he please, he may
call it _Vexillum_.) But then he is to remember, that this is only a
Controversie in _Grammar_, not in _Mathematicks_: And his Book should have
been intitled _Contra Grammaticos_, not, _Contra Geometras_. Nor is it
_Euclide_, but _Cicero_, that is concern'd, in rendring the Greek [Greek:
Semeion] by the Latine _Punctum_, not by Mr. _Hobs_'s _Signum_. The
Mathematician is equally content with either word.
What he saith here, _Chap._ 8. & 19. (and in his fifth _Dial._ p. 105. &c.)
concerning the _Angle of Contact_; amounts but to thus much, That, by the
_Angle of Contact_, he doth not mean either what _Euclide_ calls an
_Angle_, or any thing of that kind; (and therefore says nothing to the
purpose of what was in controversie between _Clavius_ and _Peletarius_,
when he says, that _An Angle of Contact hath some magnitude_:) But, that by
the _Angle of Contact_, he understands the _Crookedness of the Arch_; and
in saying, the _Angle of Contact hath some magnitude_, his meaning is, that
the _Arch of a Circle hath some crookedness_, or, is a _crooked line_: and
that, of equal Arches, That is the more crooked, whose chord is shortest:
which I think none will deny; (for who ever doubted, but that a _circular
Arch is crooked_? or, that, of such Arches, equal in length, _That is the
more crooked, whose ends by bowing are brought nearest together_?) But, why
the _Crookedness of an Arch_, should be called an _Angle of Contact_, I
know no other reason, but, because Mr. _Hobs_ loves to call that _Chalk_,
which others call _Cheese_. Of this see my _Hobbius Heauton-timorumenus_,
from _pag._ 88. to p. 100.
What he saith here of _Rations_ or _Proportions_, and their _Calculus_; for
8. Chapters together, (_Chap._ 11. _&c,_) is but the same for substance,
what he had formerly said in his 4th. Dialogue, and elsewhere. To which you
may see a full Answer, in my _Hobbius Heauton-tim._ from _pag._ 49. to p.
88. which I need not here repeat.
Onely (as a _Specimen_ of Mr. _Hobs_'s Candour, in Falsifications) you may
by the way observe, how he deals a Demonstration of Mr. _Rook_'s, in
confutation of Mr. _Hobs_'s Duplication of the Cube. Which when he had
repeated, _pag._ 43. He doth then (that it might seem absurd) change those
words, _aequales {293} quatuor cubis_ DV; (_pag._ 43. _line_ 33.) into these
(p. 44. l. 5.) _aequalia quatuor Lineis, nempe quadruplus Recta_ DV: And
would thence perswade you, that Mr. _Rook_ had assigned a _Solide_, equal
to a _Line_. But Mr. _Rook's_ Demonstration was clear enough without Mr.
_Hobse's_ Comment. Nor do I know any Mathematician (unless you take _Mr.
Hobs_ to be one) who thinks that _a Line multiplyed by a Number will make a
Square_; (what ever _Mr. Hobs_ is pleased to teach us.) But, That _a Number
multiplyed by a Number, may make a Square Number_; and, That _a Line drawn
into a Line may make a Square Figure_, _Mr. Hobs_ (if he were, what he
would be thought to be) might have known before now. Or, (if he had not
before known it) he might have learned, (by what I shew him upon a like
occasion, in my _Hob. Heaut._ _pag._ 142. 143. 144.) _How_ to understand
that language, without an Absurdity.
Just in the same manner he doth, in the next page, deal with _Clavius_, for
having given us his words, pag. 45 l. 3. 4. _Dico hanc Lineam
Perpendicularem extra circulum cadere_ (because neither _intra Circulum_,
nor in _Peripherea_;) He doth, when he would shew an errour, first make
one, by falsifying his word, _line_ 15. where instead of _Lineam
Perpendicularem_, he substitutes _Punctum A._ As if _Euclide_ or _Clavius_
had denyed the _Point A._ (the utmost point of the _Radius_,) to be in the
Circumference: Or, as if Mr. _Hobs_, by proving the _Point A._ to be in the
Circumference, had thereby proved, that the _Perpendicular Tangent A E_ had
also lyen in the Circumference of the Circle. But this is a Trade, which
Mr. _Hobs_ doth drive so often, as if he were as well faulty in his
_Morals_, as in his _Mathematicks_.
The _Quadrature of a Circle_, which here he gives us, _Chap._ 20. 21. 23.
is one of those _Twelve_ of his, which in my _Hobbius Heauton-timorumenus_
(from _pag._ 104. to _pag._ 119) are already confuted: And is the _Ninth_
in order (as I there rank them) which is particularly considered, _pag._
106. 107. 108. I call it _One_, because he takes it so to be; though it
might as well be called _Two_. For, as there, so here, it consisteth of
_Two branches_, which are Both false; and each overthrow the other. For if
the _Arch of a Quadrant_ be equal to the _Aggregate of the Semidiameter and
of the Tangent of 30. Degrees_, (as he would _Here_ have it, in _Chap._ 20.
and _There_, in the close of _Prop._ 27;) Then is it not equal to _that
Line, Whose Square is equal to Ten squares of the Semiradius_, (as,
_There_, he would have it, in _Prop._ 28. and, _Here_, in _Chap. 23._) And
if it be equal to _This_, then not to _That_. For _This_, and _That_, are
not equal: As I then demonstrated; and need not now repeat it.
The grand Fault of his Demonstration (_Chap._ 20.) wherewith he would now
New vamp his old false quadrature, lyes in those Words _Page_ 49. _line_
30, 31. _Quod Impossibile est nisi _ba_ transeat per _c_._ which is no
impossibility at all. For though he first bid us _draw the Line R c_, and
afterwards the _Line R d_; Yet, Because he hath no where proved (nor is it
true) that _these two are the same Line_; (that is, that the point _d_ lyes
in the _Line R c_, or that _R c_ passeth through _d_:) His proving that _R
d cuts off from _ab_ a Line equal to the Sine of R c_, doth not prove, that
_ab_ passeth through _c_: For this it may well do though _ab_ lye _under
c._ (vid. in case _d_ lye beyond the line _R c._ that is, further from
_A_:) And therefore, unless he first prove (which he cannot do) that _A c_
( a sixth part of _A D_) doth just reach to the line _R c_ and no further,
he only proves {294} that a sixth part of _ab_ is _equal_ to the Sine of
_B c_. But, whether it _lye above it_, or _below_ it, or (as Mr. _Hobs_
would have it) just _upon_ it; this argument doth not conclude. (And
therefore _Hugenius's_ assertion, which Mr. _Hobs_, _Chap._ 21. would have
give way to this Demonstration, doth, notwithstanding this, remain safe
enough.)
His demonstration of _Chap._ 23. (where he would prove, that _the aggregate
of the Radius and of the Tangent of 30. Degrees_ is equal to _a Line, whose
square is equal to 10 Squares of the Semiradius_;) is confuted not only by
me, (in the place forecited, where this is proved to be impossible;) but by
himself also, in this same Chap. _pag._ 59. (where he proves sufficiently
and doth confesse, that this demonstration, and the 47. _Prop._ of the
first of _Euclide_, cannot be both true.) But, (which is worst of all;)
whether _Euclid's_ Proposition be False or True, his demonstration must
needs be False. for he is in this Dilemma: If that Proposition be _True_,
his demonstration is _False_, for he grants that they cannot be both True,
_page_ 59 _line_ 21. 22. And again, if that Proposition be False, his
Demonstration is so too; for _This_ depends upon _That_, _page_ 55. _line_
22. and therefore must fall with it.
But the Fault is obvious in _His Demonstration_ (not in _Euclid's
Proposition_:) the grand Fault of it (though there are more) lyes in those
words, _page_ 56. _line_ 26. _Erit ergo M O minus quam M R_ Where, instead
of _minus_, he should have said _majus_. And when he hath mended that
Error, he will find, that the _major_ in _page_ 56. _line penult_, will
very well agree with _majorem_ in _page_ 57. _line_ 4 (where the _Printer_
hath already mended the Fault to his hand) and then the _Falsum ergo_ will
vanish.
His Section of an Angle _in ratione data_, _Chap._ 22 hath no other
foundation, than his supposed _Quadrature_ of _Chap._ 20. And therefore,
that being false, this must fall with it. It is just the same with that of
his 6. Dialogue, _Prop._ 46. which (besides that it wants a foundation) how
absurd it is, I have already shewed, in my _Hobbius Heauton-timor._ _page_
119. 120.
His _Appendix_, wherein he undertakes to shew a Method of finding _any
number of mean Proportionals, between two Lines given_: Depends upon the
supposed Truth of his 22. Chapter; about _Dividing an Arch in any
proportion given_: (As himself professeth: and as is evident by the
Construction; which supposeth such a Section.) And therefore, that failing,
this falls with it.
And yet this is other wise faulty, though _that_ should be supposed True.
For, In the first Demonstration; _page_ 67. _line_ 12. _Producta L f
incidet in I_; is not proved, nor doth it follow from his _Quoniam igitur_.
In the second Demonstration; _page_ 68. _line_ 34. 35. _Recta L f incidit
in x_; is not proved; nor doth it follow from his _Quare_.
In his third Demonstration; _page_ 71: _line_ 7. _Producta _Y P_ transibit
per _M_;_ is said _gratis_; nor is any proof offered for it. And so this
whole structure falls to the ground. And withall, the _Prop._ 47. _El._ 1
doth still stand fast (which he tells us, _page_ 59, 61, 78. must have
Fallen, if his Demonstrations had stood:) And so, _Geometry_ and
_Arithmetick_ do still agree, which (he tells us, _page_ 78: _line_ 10.)
had otherwise been at odds.
And this (though much more might have been said,) is as much as need to be
said against that Piece.
* * * * *
Printed with Licence for _John Martyn_, and _James Allestry_, Printers to
the Royal Society.
{295}
* * * * *
_Num._ 17.
PHILOSOPHICAL
_TRANSACTIONS._
* * * * *
_Munday_, _Septemb._ 9. 1666.
* * * * *
The Contents.
_Observations made in several places (at _London_, _Madrid_ and
_Paris_,) of the late _Eclipse of the Sun_, which hapned _June_ 22.
1666. Some Enquiries and Directions, concerning _Tides_, proposed by
_Dr. Wallis_. Considerations and Enquiries touching the same Argument,
suggested by Sir _Robert Moray_. An Account of several Books lately
publish't: Vid. 1. _Johannis Hevelii Descriptio Cometae,_ A. 1665.
exorti; una cum _Mantissa Prodromi Cometici_. 2. _Isaacus Vossius de
Nili & aliorum Fluminum Origine_. 3. _Le Discernement du Corps & de
l'Ame_, par Monsieur de _Cordemoy_._
* * * * *
_Observations made in several places, Of the late _Eclipse of the Sun_,
which hapned on the 22 of _June_, 1666._
The Observations that were made at _London_ by Mr. _Willughby_, Dr. _Pope_,
Mr. _Hook_, and Mr. _Philips_, are these:
The Eclipse began at 5h. 43' h. '
{ 3/11 diam. at 6. 00 | 5 dig. at 7. 06
{ 4 digits at 6. 07 | 4 dig. at 7. 13
It was { 5 dig. at 6. 13 | 3 dig. at 7. 20
darkned,{ 6 dig. at 6. 21 | 2 dig. at 7. 26
{ 7 dig. at 6. 391/2 | 1 dig. at 7. 32
{ 6 dig. at 6. 57 | 0 dig. at 7. 37
Its _Duration_ hence appears to have been one hour and 54 m. Its _greatest
Obscurity_ somewhat more than 7. digits. About the middle, between the
Perpendicular and Westward Horizontal _Radius_ the Sun, viewing it through
Mr. _Boyle_'s 60. foot-_Telescope_, there was perceived a little of the
Limb of the Moon without the Diske of the Sun: which seemed to some of the
Observers to come from some shining _Atmosphere_ about the Body either of
the Sun or Moon.
They affirm to have observ'd the _Figure_ of this _Eclipse_, and measured
the {296} _Digits_, by casting the _Figure_ through a 5 foot _Telescope_,
on an extended paper, fix't at a certain distance from the Eye-glasse, and
having a round figure; all whose _Diameters_ were divided, by 6
_Concentrick_ Circles, into 12 _Digits_.
The Observations made at _Madrid_ by a Noble Member of the _Royal Society_,
His Excellence the Earle of _Sandwich_, as they were sent to the Right
Honourable, the Lord Vice-Count _Brounker_, are these;
The Eclipse _began_ at _Madrid_ about 5 of the Clock in the morning, at 5
h. 15', the Suns _Altitude_ was 6 deg. 55'.
The _Middle_ of it was at 6 h. 2', the Suns _Altitude_, 15. deg. 5'.
The _End_ was exactly at 7 h. 5'; the Suns _Altitude_, 25. deg. 24'.
The _Duration_, 2h. 4'.