Dr. Wallis's Answer to the Foregoing Animadversions, Directed in a Letter to the Publisher, March 19. 1662/70

wish for the further clearing of this matter, that observation were made at Bristol (because there is the most considerable Flux and Reflux of any Port of England,) Whether this year 1670, the Tydes be not higher (consideratis, &c.) when the ☽ passeth ♈. ♉. and ♌, than when she passeth through the opposite signs ♉. ♊. and ♌. and particularly whether the Spring Tydes be not sensibly higher after the Change, than after the Full in February, March, and April; and higher after the Full then after the Change in August, September, and October; and also, Whether the Neap.tides in May and June rise not apparently higher than expected. I am promised, the observation shall be made here at Weymouth for this whole year round; from whence I have already received this account, that this present February 1672, the Spring-Tydes ran very high after the Change, though the weather were pretty calm, and that wind that was not very favourable to the Tydes, and that the Spring-Tydes after the Full were very low, and weak, which is exactly according to my conjecture. Dr. Wallis's Answer to the foregoing Animadversions, directed in a Letter to the Publisher, March 19. 1672. Sir, Yours with the inclosed Animadversions of M. Childrey on my Hypothesis of Tydes, came so late to hand on Thursday last (when the Post was almost ready to be gone) that I had not time, by that Post, to give you an account of them. And it is not much, I need to say now; for I do not find, that he and I are like much to disagree. That the Winds have a great influence on the Tydes of particular Coasts and Havens, according as they are more or less stiff or slack, and blow from this or that part, I do not at all question; but did always take for granted, as generally received, and upon good grounds. And the like I say of Land waters; which (though as to the Sea they signify not much in this point) are, as to In-land Rivers, very considerable; especially as to Inundations upon rising of the Water: Which is rather by Checking than Promoting the Tydes. For certainly, these Land-waters, meeting the Tyde of Flood, do hinder it from coming so far up the River as otherwise it would; and consequently, if, notwithstanding such Land-floods, flouds, the Tyde flow higher up the River than at other times, this must be derived from some other cause. But, that the Tide and Land-floud should jointly make a greater Inundation than either singly would have done, is not to be doubted. But he need not wonder, that in my Essay, though I grant both these, I said so little of either, because it was wholly beside my business; which was, to give a Statical account of Stated Periods (Diurnal, Menstrual, Annual,) arising from Regular Motions; not, of Accidental Extravagances, such as these are: And therefore I did, in the beginning of that Discourse preclude the Consideration of the Advantage or Disadvantage, which should arise from such uncertain Contingences, as Extrinsecal to that business. His third thing suggested, The Moon's Perigee; is so far from being contrary to my Hypothesis, that it is a great Part of it. And (if I do not much mis-remember,) it is, in one of my Letters to you, expressly mentioned as such. But forasmuch as it doth not still fall out at the same time of the Day, Month, or Year, I could not make it a Component of any of those noted Periods, Diurnal, Menstrual or Annual; (and of more Periods than these, I did not know that there hath been any general notice taken, of which I might think myself obliged to give an account:) but it may very well influence any or all of those, according as it falls out advantageous or disadvantageous for them. And as I do so readily concur with him in all the particulars by him suggested; so I think he will not be difficult in assenting to all the Materials of my Hypothesis. The account which I give of the Diurnal and Menstrual Periods (from the Common Center of Gravity of the Earth and Moon,) he doth allow as very Rational: And consequently (which is the Foundation of it,) that any Acceleration or Retardation of the Compound motion of the particular parts in the Earth's Surface, is to give such an Accumulation of waters as causeth a Tyde; and the Complication of such Accelerations and Retardations, concurring or interfering one with another, doth occasion the perplex Varieties in them: Of which therefore there is no clear account to be given, without considering severally the proper Effects of each, from whence doth result the Compound Effect of all together. Now as to the two most signal motions of the Earth, the Diurnal if we suppose them each in themselves Equal, and both perfectly circular and upon Parallell Axes, though neither of them singly consider'd, would give an Inequality of motion; yet the compound of both together, being swiftest at Midnight and slowest at Noon, (because the compound of both is, in that, the Aggregate, in this, the difference of them) would give us two Tydes in each Diurnal Revolution: But those alwayes at Noon, and Midnight. If to these we add the Menstrual, whereby the Earth describes a small Epicycle about the Common Center of Gravity of the Earth and Moon; and suppose this also Equal in itself, and Circular, about an Axe parallell to the rest: neither would this, of itself, give any Inequality; but, compounded with the rest, it will. For, this compounded with the Annual, doth, at the New Moon, increase; at the Full, abate of that motion, as to all parts of the Earth's Surface: But compounded with the Diurnal (which, in this case, is much the more considerable, as recurring every day,) it doth most add to, or abate of, that motion, as to each particular place of the Earth's Surface, when the Moon is in the Meridian of that place, below or above the Horizon; and would therefore, at those times, give us two Tydes. (For which, and other particulars of like nature, that they may be the better apprehended, I refer myself to the Inspection of the Schemes pertaining to my Hypothesis.) Now because this coming of the Moon to the Meridian, above and below the Horizon, or (as Sea men call it) the Moon's Southing and Northing, doth, in a Month's time, pass round the whole circle of 24 hours; hence it comes to pass, that the time of the Tydes doth so also: Which I take to be the true Account of the Menstrual period. And because this Composition of the Menstrual with the Diurnal (which seems by the Effect to be most predominant, though not to extinguish the other,) casts the time at the Moon's being in the Meridian; and that of the Annual and Diurnal, when the Sun is in the Meridian: When both these happen at the same time, as at the Full and Change of the Moon; the Tydes must needs be the greater: Which I take to be the true Account of the spring-Tydes, and Neap-Tydes. And thus far (which is the main of my Hypothesis,) he concurs with me, as having given at least a very Rational and Probable Account. If therefore there be no other Periods of Tydes but these; or no other remarkable, my work is done, and I need not be further solicitous: For, then there will seem to be either no other inequality of motions, or none considerable. But, if there be also observable an Annual period, (as very many think there is;) or any other such period, (as perhaps there may be,) then are we to seek for the Cause thereof in somewhat of Inequality, which doth (for the Annual Period) Annually recur; or (for any other Period,) which doth recur in such a time as that other Period doth require. Now forasmuch as the three Motions above mentioned are neither (as was above supposed) each Equal in itself, or perfectly Circular, nor all on Parallel Axes; there is, both as to the Sun, and as to the Moon, at least a double Inequality; the one, by reason of the Excentricity, and (which depends thereon) the Apogeeum and Perigeum; the other, by reason of the Obliquity of the Zodiack and the Moon's Orbite, with the Equinoctial, and with each other. From every of which doth proceed some little Inequality of Motion in the Earth's Surface: But whether so much as to make any remarkable alteration in the Tydes, is hardly determinable than by observation. Now for that of the Moon, both as to its Apogeeum and Perigeum, (with the Inequality of Motion depending on it;) and as to the Obliquity of its Orbe both with the Zodiack and the Equator (which causeth another Inequality both in the Motion of Longitude and Right Ascension,) I have hitherto contented myself to insinuate it, in one of my Letters on this subject, without further insisting on it; because I did not know of any Periodical Vicissitude of Tydes consonant thereunto. When any such shall be discovered, we have here a Foundation ready for the Salving of it. But as to any Annual Vicissitude, it is not of use, because it doth not Annually recur. But, because it hath been almost generally received, That there is an Observable Annual Period; I did, for the salving of that, apply not the Inequality of the Natural Dayes, but those causes from whence that proceeds, the Excentricity of the Sun or Earth's Orb, and the Obliquity of the Zodiack. The former of these, if singly considered, would cast those Annual Tydes in June and December (the times of the Sun's Apogeeum and Perigeum, or rather the Earth's Aphelium and Perielium, when are the slowest and the swiftest Annual motions in the Zodiac: ) the latter, if considered alone, would cast them upon the two Equinoxes, and the two Solstices, (the times of the Least and of the Greatest Right Ascensions:) But if both be jointly considered, they must cast these (as they do the greatest Inequality of the Natural days) at some intermediate times, between the Autumnal Equinox in September, and the Perigeeum in December; and again, between this Perigeeum, and the following Vernal Equinox in March: As is more than probable (without the trouble of any new computation) from the greatest Inequality of the Natural Days, arising from the same causes: But whether precisely at the same time with that Inequality, or whether in all parts of the world at any one time, I do not undertake there to determine; but rather believe the contrary, because the different Position of places may very much alter the Influence of both or either Causes. I did only mention, as a thing very notorious, that it doth so constantly fall out on the coasts of Kent; and particularly of Romney-marsh, about Allhallontide and Candlemas. This Account of the Annual Vicissitude is that only, to which M. Childrey doth except; opposing first, the Judgement of Seamen (more considerable than that of the Inhabitants of Romney-Marsh,) who use to say, either that the time of the year signifies nothing; or, if at all, it is about the Equinoxes. Then, that if this be the cause, it will be constant, and that in February as well as in November. And thirdly, that the Seamen about Weymouth have not observed any thing signal about those Times. To the first, I answer; if not then, but at the Equinoxes, then so much of the Hypothesis as concerns the Excentricity may be spared, (or allowed to be so little as not to be remarkable;) and that of the Obliquity alone will give a sufficient account of it. Or if (to which he seems rather to incline,) there be no such Annual Vicissitudes at all; then may that of the Obliquity be spared also, and the Hypothesis perfect without it. And, till some such be observed and acknowledged, it will be sufficient to say, That, though both the Excentricity and Obliquity do cause some Inequality in the Motion; yet so little, as that in the Tydes it is not remarkable, they falling just as if the three Motions, (Annual, Menstrual, Diurnal,) were all exactly Circular, and on Parallel Axes. To the second, which concerns matter of Fact in Rumney-Marsh; I say, that (according to the best account I can there get, and the unanimous consent as well of Fisher-men and other Water-men, as of other Inhabitants,) it is constant; hardly missing (or very seldom) any one year (be the weather fair or foul;) and as well about Candlemas, as about Allhallontide, every year, though not then so high: Of which (though they do not pretend to give any reason of it,) I think a Cause may be very rationally assigned. For, if you consult the Tables of the Inequality of Natural Days (which parallel I make use of for the Explication of this,) you will find, that about one of the Extreams (in January) the Increase and Decrease of the Natural Days fluctuates very much; sometime increasing, sometime decreasing, according as this or that of the two Causes, thwarting one another, doth prevail: But about the other Extream (in October,) it is much otherwise; the Increasing and Decreasing going on in a continual course for a long time together. And the same Causes, applyed to the business of Tydes, may very rationally be supposed to produce as unequal effects. To the third, That the Sea-men at Weymouth have not observed any such signal Effects about Allhallontide and Candlemas: It is very possible that they have not, and that nothing signal on those Coasts useth to happen at those times: For, I fix that matter of Fact principally on Rumney-Marsh, (and that it doth there constantly happen, I am pretty well out of doubt,) and do but by conjecture extend it to the River of Thames (as having its Mouth not far from those Coasts,) where yet, I think, you can be my Witness, that it hath been observed several years to succeed accordingly. What variety is on other Coasts, I am not certain: But (from an Account read in the R. Society in my hearing, about the end of the year 1667,) I understand that about Chepstow-bridge (and consonantly, I suppose, on the Severne at other places,) they observe the like to happen about the beginning of March, and end of September, (the one as much before the Vernal, as the other is after the Autumnal Equinox, like as in our case it happens,) which they call by the name of St. David's stream, and Michaelmas-stream; as we do those in Kent, Candlemas stream, and Allhallon-stream: (And when Sea-men take so much notice of particular Tydes as to give names to them, 'tis a great presumption, that it is for some remarkable kable Accident usually happening at those Seasons.) Of these different Seasons at Chepstow bridge from those of Rumney Marsh, I gave you my remarks in a Letter of mine to you in March following. And the like differences, I suppose, will be observable on other Coasts, according as their positions be advantageous or disadvantageous to the one or the other of the two Causes, on which this Phenomenon depends. But since it is not yet (it seems) agreed, Whether such an Annual Phenomenon do happen; or, if so, not at that time; (so that, for ought yet appears, it may be at the Seasons I design, that is, between the Winter-Solstice and the two Equinoxes on either side of it; though, on several Coasts, severally remote,) I think it best to let this part of the Hypothesis stand as it is, unrevoked, as that, which, when it shall be discovered and agreed on, stands ready enough to give a rational account of it, and, in the mean time, does no hurt. And in such a Complication of Causes so abstruse, scarce anything but Observation will determine, which of the Causes, and in what degree, is to be Judged predominant. And if to this of the Sun's or Earth's, be added that of the Obliquity and Eccentricity of the Moon's Orbit. (of which, for the reason above-mentioned, I had taken so little notice,) it will, if it do no good, at least do no hurt. And I the rather think, it may be considerable, because the Earth and Moon's Appropinquation and Elongation, doth really alter the Distance of the Common Center of Gravity (of the Earth and moon) from the Earth (rendering the Earth's Epicycle Elliptical;) and much favors what M. Childrey observes of the Moon in Perigee. And this is the sum of what I thought proper to return you, upon those Animadversions, being, &c. An Accomp of some Books. I. DISSEXTATIONES MEDICAE TRES: 1. De Causis fluxus Menstrui Mulierum. 2. De Sympathia variarum Corporis partium cum Utero. 3. De Usu Lactis ad tabidos reficiendos, & de immediato Corporis Alimento. Auth. Francisco Bayle, Doct. Medico. Tolosae, 1670. in 4°. His Ingenious Author to prepare his Reader to a candid reception of these Discourses, represents in the Preface, how much mischief and prejudice hath been done to knowledge both by