John Wallis

Philip Beeley and Christoph J. Scriba (eds), Correspondence of John Wallis (1616–1703), Vol. 3: October 1668–1671

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149.Wallis to Henry OldenburgOxford, 19/[29] March 1669/[1670]


W Letter sent: London Royal Society Early Letters W1, No. 104, 4 pp. (our source). At top of p. 1 in Oldenburg's hand: 'Dr Wallis's Answer to Mr Childreys Animadversions on his Theory of Tydes.' and 'Read Mar. 24. 69. Enter'd LB. 3. 355.'—printed: Oldenburg, Correspondence VI, 578–84.

w1 Copy of letter sent: London Royal Society Letter Book Original 3, pp. 355–63.

w2 Copy of w1: London Royal Society Letter Book Copy 3, pp. 440–50.

E 1 First edition: Philosophical Transactions No. 64 (10 October 1670), 2068–74 ('Dr. Wallis's Answer to the foregoing Animadversions, directed in a Letter to the Publisher, March 19. 1669/70.').

E 2 Second edition (partly): The Philosophical Transactions and Collections …Abridged and Disposed under General Heads I, 520–3.

Reply to: Childrey–Ward 4/[14].III.1669/70.

This letter represents Wallis's reply to Childrey's animadversions on his hypothesis of tides, which had been forwarded to him by Oldenburg on 16 March or just before. Oldenburg pg 328read the present letter at the meeting of the Royal Society on 24 March, when it was also ordered that a copy be sent to Childrey. See Birch, History of the Royal Society II, 431.

1Oxford. March 19. 1669./70. Saturday.


3Yours794 with the inclosed Animadversions795 of Mr Childrey on my Hypoth-4esis796 of Tydes, came so late to hand on Thursday last,797 (when the Post 5was allmost ready to be gone,) that I had not time, by that Post, to give Critical Apparatus6you an account of them. And it is not much that I need to say now. For I 7do not find, that hee & I are like much to disagree.

8That the Winds have a great influence on the Tides of particular Coasts 9& Havens; according as they are more or lesse stiff or slack, & do blow from 10this or that part: I do not at all question. But did allways take for granted, 11as generally received, & upon good grounds.

12And the like I say of Land-waters: which (though as to the Sea they doe 13not signify much in this Point) are, as to In-land Rivers, very considerable; 14especially as to Inundations upon rising of the Water: Which is rather by 15Checking than Promoting the Tides. For, certainly, these Land-waters, meet-16ing the Tide of Floud, do hinder it from coming so far up the River as other-17wise it would. And, consequently, if notwithstanding such Land-flouds, the 18Tide flow higher up the River than at other times, this must be derived from 19some other cause. But, that the Tyde & Land-floud should jointly make a 20greater Inundation than either singly would have done, is not to be doubted.

21But hee need not wonder that, in my Essay,798 though I grant both 22these, I sayd so little of either; Because it was wholly beside my business; 23which was, to give a statical account of Stated Periods (Diurnal, Menstrual, 24Annual,) arising from Regular Motions: not, of Accidental Extravagances, 25such as these are. And therefore I did, in the beginning of that discourse 26preclude the consideration of the Advantage or Disadvantage which should 27arise from such uncertain contingences, as extrinsecal to that busyness.

pg 3291His third thing Suggested, The Moones Perigaeosis; is so far from being 2contrary to my Hypothesis, that it is a part of it. And (if I do not much 3mis-remember) it is, in one of my letters to you, expressely mentioned as 4such. But for as much as it doth not still fall out at the same time of the Day, 5Moneth, or Year; I could not make it a Component of any of those noted 6periods, Diurnal, Menstrual, or Annual; (& of more Periods than these, I did Critical Apparatus7not know that there hath been any generall notice taken, of which I might 8think myself obliged to give an account:) But it may very well influence any 9or all of these, according as it falls out advantageous or disadvantageous for 10them.

11And as I do so readyly concur with him in all the particulars by him 12suggested; so I think he will not be difficult in assenting to all the Materials 13of my Hypothesis.

14The Account which I give of the Diurnal & Menstrual Periods (from the 15Common Center of Gravity, of the Earth & Moon,) hee doth allow as very 16Rational. And consequently (which is the foundation of it) that any Acceler-17ation or Retardation of the Compound Motion of the particular parts in the 18Earths Surface, is to give such an Accumulation of waters as causeth a Tyde. 19And the complication of such Accelerations & Retardations, concurring or 20enterfeering one with another, doth occasion the perplex Varieties in them. 21Of which therefore there is no clear account to be given, without considering 22severally the proper Effects of each; from whence doth result the Compound 23Effect of all together.

24Now as to the two most signal motions of the Earth, the Diurnal & 25Annual; if we suppose them each in themselves equal, & both perfectly 26Circular & upon Parallel Axes; though neither of them singly considered 27would give any Inequality of Motion; yet the Compound of both together, 28being Swiftest at Mid-night, & Slowest at Noon, (because the Compound 29of both is, in that, the Aggregate; in this, the Difference of them;) would 30give us two Tides in each Diurnal Revolution: But those allways at Noon, 31& Midnight.

32If, to these, wee adde the Menstrual; whereby the Earth describes a 33smal Epicycle about the Common Center of gravity of the Earth & Moon; Critical Apparatus34& suppose this allso Equal in itselfe, and Circular, about an Axe parallel to 35the rest: Neither would this, of itself, give any Inequality: But, compounded 36with the rest, it will. For this compounded with the Annual; doth, at the 37New-Moon, Increase; at the Full-moon, Abate, of that Motion; as to all pg 3301parts of the Earths Surface: But, compounded with the Diurnall, (which, in 2this case, is| much the more considerable, as recurring every day,) it doth [2] 3most Adde to, or Abate of, that Motion, as to each particular place of the 4Earths Surface, when the Moon is in the Meridian of that place, Below or 5Above the Horizon; & would therefore, at those times, give us two Tides. Critical Apparatus6(For which, & other particulars of like nature, that they may be the better 7apprehended, I refer myself to the inspection of the Schemes pertaining to my 8Hypothesis.)

9Now because this coming of the Moon to the Meridian, above or below 10the Horizon, or (as the Seamen call it) the Moons Southing & Northing, 11doth, in a Moneths time, passe round the whole circle of 24 hours: hence it 12comes to pass, that the Time of the Tydes doth so allso. Which I take to 13be the true account of the Menstrual period. And because this composition 14of the Menstrual with the Diurnal (which seemes by the effect to be most 15predominant, though not to extinguish the other,) casts the time at the 16Moons being in the Meridian: and that of the Annual & Diurnal; when the 17Sun is in the Meridian: When both these happen at the same time, as at the 18Full & Change of the Moon; the Tides must needs be the Greater. Which I 19take to be the true account of the Spring-tides, & Neap-tides.

20And thus far, (which is the Main of my Hypothesis,) hee concurs with 21mee, as having given at lest a very Rational & Probable account.

22If therefore there be no other Periods of Tydes but these; or, no other 23remarkable: My work is done, & I need not be further solicitous. For then 24there will seem to be either no other inequalitie of motions, or none con-25siderable. But if there be allso observable an Annual period, (as very many 26think there is;) or any other such Periode, (as perhaps there may bee:) then 27are wee to seeke for the cause thereof in somewhat of inequality which doth 28(for the Annual Period) Annually recur; or (for any other periode) which 29doth recur in such a time as that other periode doth require.

30Now forasmuch as the three Motions above mentioned, are neither (as 31was above supposed) each equal in itself, or perfectly circular; nor, all on 32parallel Axes: there is, both as to the Sun, & as to the Moon, at lest a 33double inequality; the one by reason of the Excentricity, & (which depends 34thereon) the Apogaeum & Perigaeum; the other by reason of the Obliquity 35of the Zodiack & the Moons Orbit, with the Equinoctial, & with each other. 36From every of which doth proceed some little inequality of motion in the 37Earths Surface. But, whether so much as to make any remarkable alteration 38in the Tides; is hardly otherwise determinable than by Observation.

pg 3311Now for that of the Moon, both as to its Apogaeum & Perigaeum, (with 2the inequality of motion depending on it:) and as to the Obliquity of its Orb, Critical Apparatus3both with the Zodiack & the Equator, (which causeth another inequality 4both in the Motion of Longitude & Right-Ascension;) I have hitherto con-5tented myself onely to insinuate it, in one of my letters on this subject, 6without further insisting on it: Because I did not know of any Periodical 7Vicissitude of Tydes consonant thereunto. When any such shal be discov-8ered; we have here a foundation ready for the salving of it. But as to any 9Annual vicissitude, it is not of use; because it doth not Annually recurre.

10But, because it hath been, allmost, generally received, That there is 11an observable Annual Period: I did, for the salving of that, apply, (not the 12Inequality of the Natural days, but those causes from whence that proceedes) 13the Excentricity of the Sun or Earths Orb, & the Obliquity of the Zodiack.

14The Former of these, if singly considered, would cast those Annual 15Tides in June & December, (the times of the Suns Apogaeum & Perigaeum, 16or rather the Earths Aphelium & Perihelium, when are the slowest & the 17swiftest Annual Motions in the Zodiack:) The Latter, if considered alone, 18would cast them upon the two Equinoxes, & the two Solstices, (the times 19of the Lest & of the Greatest Right-Ascensions:) But if both be jointly con-20sidered; they must cast these (as they do the greatest Inequalitie of the 21Natural days) at some intermediate times, between the Autumnal Equinox 22in September, & the Perigaeum in December; and again, between this Peri-23gaeum, & the following Vern al Equinox in March. As is more than probable 24(without the trouble of any new Computation) from the greatest inequalitie 25of the Natural Days, arising from the same causes. But whether precisely at 26the same time with that Inequality, or whether in all parts of the World at 27any one Time; I do not undertake there to determine: But do rather beleeve 28the contrary; because the different position of places, may very much alter 29the influence of both or either causes. I did onely mention, as a thing very 30notorious, that it doth so constantly fall out on the coasts of Kent, & par-31 [3] ticularly of Rumney-Marsh, about Allhollantide & Candlemas.|

32This Account of the Annual vicissitude, is that onely to which hee doth 33except. Opposing, first the judgement of Sea-men, (more considerable than 34that of the Inhabitants of Rumney-Marsh,) who use to say, either that the 35time of the year signifies nothing; or, if at all, it is about the Equinoxes. 36Then, that if this be the cause, it will be constant; & that, in February as 37well as in November. And thirdly, that the Seamen about Weymouth have 38not observed anything signal about those times.

pg 3321To the first, I answere; If not then, but at the Equinoxes: then so much 2of the Hypothesis as concerns the Excentricity; may be spared; (or allowed 3to be so little as not to be remarkable;) and that of the Obliquity alone, will 4give a sufficient account of it. Or if (to which hee seemes rather to incline) 5there be no such Annual Vicissitude at all; then may that of the Obliquity 6be spared allso; & the Hypothesis perfect without it. And, till some such be Critical Apparatus7observed & acknowledged; it will be sufficient to say, that though both the 8excentricity & the Obliquity do cause some inequality in the motion; yet, so Critical Apparatus9little, as that in the Tides it is not remarkable; they falling, just as if the 10three Motions (Annual, Menstrual, & Diurnal,) were all exactly circular, & 11on Parallell Axes.

12To the second; which concerns matter of fact in Rumney-Marsh.799 I 13say that (according to the best account I can there get, & the unanimous 14consent as well of Fisher-men, & other Water-men, as of other Inhabitants) it 15is constant; hardly missing (or very seldome) any one year; (be the weather 16fair or foul:) and as well, about Candlemas, as about Alhollantide, every 17year; though not then so high. Of which (though they do not pretend to 18give any reason of it) I think a cause may be very rationally assigned. For 19if you consult the tables of the Inequality of Natural days (which parallell 20I make use of for the explication of this,) you will find that about one of 21the extreemes (in January) the increase & decrease of the Natural days 22fluctuates very much; sometime increasing, sometime decreasing, according 23as this or that of the two causes, thwarting one another, doth prevail: But 24about the other extreme, (in October,) it is much otherwise; the increasings 25& decreasings going on in a continual course for a long time together. And 26the same causes, applyed to the business of Tides, may very rationally be 27supposed to produce as unequal effects.

28To the third, That the Sea-men at Weymouth have not observed any 29such signal effects about Allhollandtide & Candlemas: It is very possible that 30they have not, & that nothing signal on those coasts doth use to happen at 31those times: For I fix that matter of fact, principally, on Rumney-Marsh, (& 32that it doth there constantly happen, I am pretty well out of doubt,) & do 33but by conjecture extend it to the River of Thames, (as having its mouth 34not far from those coasts,) where yet, I think, you can be my witness, that 35you have observed it several years to succeed accordingly. What variety is pg 3331on other coasts, I am not certain: But (from an account800 read in the R. 2Society in my hearing, about the end of the year 1667) I understand, that, 3about Chepstow-bridge (& consonantly, I suppose, on the Severn at other 4places,) they observe the like to happen about the beginning of March & end 5of September, (the one about as much before the Vernal, as the other is after 6the Autumnal Equinox, like as in our case it happens,) which they call by 7the name of St Davids-stream, and Michaelmas-stream; as wee do those in Critical Apparatus8Kent, Candelmas-stream and Allholland-stream: (And, when Sea-men take 9so much notice of particular Tides as to give names to them; 'tis a great 10presumption, that it is for some remarkable accident usually happening at 11those seasons.) Of these different seasons at Chepstow-bridge from those 12of Rumney-marsh, I gave you my remarks in a letter of mine801 to you in 13March following. And the like differences, I suppose, will be observable on 14other coasts, according as their positions be advantageous or disadvanta-15geous to the one or the other of the two causes on which this Phaenomenon 16doth depend.

17But since it is not yet (it seemes) agreed, whether such Annual Phaeno-18mena do happen; or, if so, not at what time; (so that, for ought that appears, 19it may be at the seasons I design; that is, between the Winter Solstice & 20the two Equinoxes on either side of it; though, on severall coasts, severally 21remote:) I think it best to let this part of the Hypothesis stand as it is, 22 [4] unrevoked.|

23As that which, when it shal bee discovered & agreed on, stands ready 24inough to give a rational account of it; &, in the mean time, doth no hurt. 25And, in such a complication of causes so abstruse, scarce any thing, but 26observation, wil determine, which of the causes, & in what degree, is to be 27judged predominant.

28And if to this of the Suns or Earths, be added that of the Obliquity & 29Excentricity of the Moons Orbit, (of which, for the reason above mentioned, 30I had taken so little notice,) it will, if it do no good, at lest do no hurt. And 31I do the rather think it may be considerable; because the Earth & Moons 32Appropinquation & Elongation, doth really alter the distance of the common Critical Apparatus33Center of gravity (of the Earth & Moon) from the Earth; (rendering the pg 3341Earths Epicycle Elliptical:) and much to favour what Mr Childrey observes 2of the Moon in Perigaeo.

3And this is the summe of what I thought proper to return you (upon Critical Apparatus4those Animadversions) being

  • 5Sir,                                
  • 6Your friend to serve you,
  • 7John Wallis.

  • 8These
  • 9For Mr Henry Oldenburg, at his
  • 10house in the Palmal, near St
  • 11James's
  • 12London.

Notes Settings


Editor’s Note
794 Yours: i.e. Oldenburg–Wallis c.16/[26].III.1669/70.
Editor’s Note
795 Animadversions: i.e. Childrey–Ward 4/[14].III.1669/70.
Editor’s Note
796 Hypothesis: i.e. Wallis, 'An Essay of Dr John Wallis, exhibiting his Hypothesis about the Flux and Reflux of the Sea', Philosophical Transactions No. 16 (6 August 1666), 263–81; Wallis, Correspondence I, 200–22.
Editor’s Note
797 Thursday last: i.e. 17 March 1669/70.
Critical Apparatus
6 I (1) intend (2) need
Editor’s Note
798 Essay: i.e. Wallis–Boyle 25.IV/[5.V].1666 (Wallis, Correspondence II, 200–22), published in Philosophical Transactions No. 16 (6 August 1666), 263–81 ('An Essay of Dr John Wallis, exhibiting his Hypothesis about the Flux and Reflux of the Sea').
Critical Apparatus
34 Axe (1) equal (2) parallel
Critical Apparatus
7 to say add.
Critical Apparatus
9–11 they falling … Parallell Axes. add.
Editor’s Note
799 Rumney-Marsh: i.e. Romney Marsh.
Editor’s Note
800 Account: Wallis refers to this account in Wallis–Oldenburg 7/[17].III.1667/8 (Wallis, Correspondence II, 437). The meeting concerned had probably taken place more than a year earlier in December 1666.
Critical Apparatus
8 And (1) 'tis a great presumption, (2) when Sea-men
Editor’s Note
801 letter of mine: i.e. Wallis–Oldenburg 7/[17].III.1667/8 (Wallis, Correspondence II, 435–9).
Critical Apparatus
33 Earth; (1) & render (2) (rendering
Critical Apparatus
4 Animadversions) (1) from (2) being
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