Chapter III: Appendix (2)

Now by the Hypothesis it is evident, that the Water in _Z_, being nearer, is more drawn by the Moon, than the Center of the Earth _C_, and that again more than the Water in _N_; wherefore the Water in _Z_ hath a tendency towards the Moon, contrary to that of Gravity, being equal to the excess of the Gravitation in _Z_, above that in _C_: And in the other case, the Water in _N_, tending less towards the Moon than the Center _C_, will be less pressed, by as much as is the difference of the Gravitation towards the Moon in _C_ and _N_. This rightly understood, it follows plainly, that the Sea, which otherwise would be Spherical, upon the Pressure of the Moon, must form it self into a Spheroidal or Oval Figure, whose longest Diameter is where the Moon is vertical, and shortest where she is in the Horizon; and that the Moon shifting her Position as she turns round the Earth once a Day, this Oval of Water shifts with her, occasioning thereby the two Floods and Ebbs observable in each 25 Hours.

And this may suffice, as to the general Cause of the Tides; it remains now to shew how naturally this Motion accounts for all the Particulars that have been observ'd about them; so that there can be no room left to doubt, but that this is the true cause thereof.

The Spring Tides upon the New and Full Moons, and Neap Tides on the Quarters, are occasion'd by the attractive Force of the Sun in the New and Full, conspiring with the Attraction of the Moon, and producing a Tide by their united Forces: Whereas in the Quarters, the Sun raises the Water where the Moon depresses it, and the contrary; so as the Tides are made only by the difference of their Attractions. That the force of the Sun is no greater in this Case, proceeds from the very small Proportion the Semi-diameter of the Earth bears to the vast distance of the Sun.

It is also observ'd, that _cæteris paribus_, the Æquinoctial Spring Tides in _March_ and _September_, or near them, are the Highest, and the Neap Tides the lowest; which proceeds from the greater Agitations of the Waters, when the fluid _Spheroid_ revolves about a great Circle of the Earth, than when it turns about in a lesser Circle; it being plain that if the Moon were constituted in the Pole, and there stood, that the _Spheroid_ would have a fix'd Position, and that it would be always high Water under the Poles, and low Water every where under the Æquinoctial: And therefore the nearer the Moon approaches the Poles, the less is the agitation of the Ocean, which is of all the greatest, when the Moon is in the Æquinoctial, or farthest distant from the Poles. Whence the Sun and Moon, being either conjoined or opposite in the Æquinoctial, produce the greatest Spring Tides; and the subsequent Neap Tides, being produc'd by the Tropical Moon in the Quarters, are always the least Tides; whereas in _June_ and _December_, the Spring Tides are made by the Tropical Sun and Moon, and therefore less vigorous; and the Neap Tides by the Æquinoctial Moon, which therefore are the stronger: Hence it happens, that the difference between the Spring and Neap Tides in these Months, is much less considerable than in _March_ and _September_. And the reason why the very highest Spring Tides are found to be rather before the Vernal and after the Autumnal Equinox, _viz._ in _February_ and _October_, than precisely upon them, is, because the Sun is nearer the Earth in the Winter Months, and so comes to have a greater effect in producing the Tides.

Hitherto we have consider'd such Affections of the Tides as are Universal, without relation to particular Cases; what follows from the differing Latitudes of places, will be easily understood by the following Fig. (_Vide Fig. 2. Plate 1._)

Let _ApEP_ be the Earth cover'd over with very deep Waters, _C_ its Center, _P_, _p_, its Poles, _AE_ the Æquinoctial, _F_, _f_, the parallel of Latitude of a Place, _D_, _d_, another Parallel at equal distance on the other side of the Æquinoctial, _H_, _h_, the two Points where the Moon is vertical, and let _K_, _k_, be the great Circle, wherein the Moon appears Horizontal. It is evident, that a Spheroid describ'd upon _Hh_, and _Kk_, shall nearly represent the Figure of the Sea, and _Cf_, _CD_, _CF_, _Cd_, shall be the heighths of the Sea in the places _f_, _D_, _F_, _d_, in all which it is High-water: And seeing that in twelve Hours time, by the diurnal Rotation of the Earth, the Point _F_ is transferr'd to _f_, and _d_ to _D_: The height of the Sea _CF_ will be that of the High-water when the Moon is present, and _Cf_ that of the other High-water, when the Moon is under the Earth: Which in the case of this Figure is less than the former _CF_. And in the opposite Parallel _Dd_, the contrary happens. The Rising of the Water being always alternately greater and less in each place, when it is produc'd by the Moon declining sensibly from the Æquinoctial; that being the greatest of the two High-waters in each diurnal Revolution of the Moon, wherein she approaches nearest either to the Zenith or Nadir of the place: Whence it is, that the Moon in the Northern Signs, in this part of the World, makes the greatest Tides when above the Earth, and in Southern Signs, when under the Earth; the Effect being always the greatest where the Moon is farthest from the Horizon, either above or below it. And this alternate Increase and Decrease of the Tides has been observ'd to hold true on the Coast of _England_, at _Bristol_ by Captain _Sturmy_, and at _Plymouth_ by Mr. _Colepresse_.

But the Motions hitherto mentioned are somewhat alter'd by the Libration of the Water, whereby, though the Action of the _Luminaries_ should cease, the Flux and Reflux of the Sea would for some time continue: This Conservation of the impress'd Motion diminishes the differences that otherwise would be between two consequent Tides, and is the reason why the highest Spring-Tides are not precisely on the New and Full Moons, nor the Neaps on the Quarters; but generally they are the third Tides after them, and sometimes later.

All these things would regularly come to pass, if the whole Earth were cover'd with Sea very deep; but by reason of the shoalness of some places, and the narrowness of the Streights, by which the Tides are in many cases propagated, there arises a great diversity in the Effect, and not to be accounted for, without an exact Knowledge of all the Circumstances of the Places, as of the Position of the Land, and the Breadth and Depth of the Channels by which the Tide flows; for a very slow and imperceptible Motion of the whole Body of the Water, where it is (for Example) 2 Miles deep, will suffice to raise its Surface 10 or 12 Feet in a Tides time; whereas, if the same quantity of Water were to be convey'd up a Channel of 40 Fathoms deep, it would require a very great Stream to effect it, in so large Inlets as are the Channel of _England_, and the _German_ Ocean; whence the Tide is found to set strongest in those places where the Sea grows narrowest; the same quantity of Water being to pass through a smaller Passage: This is most evident in the _Streights_, between _Portland_ and _Cape de Hague_ in _Normandy_, where the Tide runs like a Sluce; and would be yet more between _Dover_ and _Calais_, if the Tide coming about the Island from the North did not check it. And this force being once impress'd upon the Water, continues to carry it above the level of the ordinary height in the Ocean, particularly where the Water meets a direct Obstacle, as it is at St. _Malo's_; and where it enters into a long Channel, which running far into the Land, grows very streight at its Extremity; as it is in the _Severn-Sea_ at _Chepstow_ and _Bristol_.

This shoalness of the Sea, and the intercurrent Continents are the reason, that in the open Ocean the time of High water is not at the Moons appulse to the Meridian, but always some Hours after it; as it is observ'd upon all the West Coast of _Europe_ and _Africa_, from _Ireland_ to the _Cape of Good Hope_: In all which a S. W. Moon makes High-water, and the same is reported to be on the West side of _America_. But it would be endless to account all the particular Solutions, which are easie Corollaries of this _Hypothesis_; as why the _Lakes_, such as the _Caspian Sea_, and _Mediterranean Seas_, such as the _Black Sea_, the _Streights_ and _Baltick_, have no sensible Tides: For _Lakes_ having no Communication with the Ocean, can neither increase nor diminish their Water, whereby to rise and fall; and Seas that communicate by such narrow Inlets, and are of so immense an Extent, cannot in a few Hours time receive or empty Water enough to raise or sink their Surface any thing sensibly.

Lastly, to demonstrate the Excellency of this Doctrine, the Example of the Tides in the Port of _Tunking_ in _China_, which are so extraordinary, and differing from all others we have yet heard of, may suffice. In this Port there is but one Flood and Ebb in 24 Hours; and twice in each Month, _viz._ when the Moon is near the Æquinoctial there is no Tide at all, but the Water is stagnant; but with the Moons Declination there begins a Tide, which is greatest when she is in the Tropical Signs: Only with this difference, that when the Moon is to the Northward of the Æquinoctial, it Flows when she is above the Earth, and Ebbs when she is under, so as to make High-water at Moons-setting, and Low-water at Moons-rising: But on the contrary, the Moon being to the Southward, makes High-water at rising, and Low-water at setting; it Ebbing all the time she is above the Horizon. As may be seen more at large in the _Philosophical Transactions_, Numb. 162.

The Cause of this odd Appearance is propos'd by Mr. _Newton_, to be from the concurrence of two Tides; the one propagated in six Hours out of the great _South-Sea_ along the Coast of _China_; the other out of the _Indian-Sea_, from between the Islands in twelve Hours, along the Coast of _Malacca_ and _Cambodia_. The one of these Tides, being produc'd in North Latitude, is, as has been said, greater, when the Moon being to the North of the Equator is above the Earth, and less when she is under the Earth. The other of them, which is propagated from the _Indian Sea_, being raised in South-Latitude, is greater when the Moon declining to the South, is above the Earth, and less when she is under the Earth: So that of these Tides alternately greater and lesser, there comes always successively two of the greater and two of the lesser together every Day; and the High-water falls always between the times of the arrival of the two greater Floods; and the Low-water between the arrival of the two lesser Floods. And the Moon coming to the Æquinoctial, and the alternate Floods becoming equal, the Tide ceases, and the Water stagnates: But when she has pass'd to the other side of the Equator, those Floods which in the former Order were the least, now becoming the greatest, that That before was the time of High-water, now becomes the Low-water, and the Converse. So that the whole appearance of these strange Tides, is without any forcing naturally deduc'd from these Principles, and is a great Argument of the Certainty of the whole _Theory_.

_A Theory of the _Variation_ of the _Magnetical Compass_. By Mr. _Ed.
Halley_, Fellow of the Royal Society._

The Variation of the Compass (by which I mean the Deflection of the Magnetical Needle from the true Meridian) is of that great Concernment in the Art of Navigation, that the neglect thereof, does little less than render useless one of the noblest Inventions Mankind ever yet attained to. And for this cause all Ships of Consequence (especially those bound beyond the Equator) carry with them Instruments on purpose to observe this Variation: That so the Course steer'd by the Compass, may be reduc'd to the true Course in respect of the Meridian.

Now although the great utility that a perfect Knowledge of the Theory of the Magnetical Direction would afford to Mankind in general, and especially to those concern'd in Sea Affairs, seems as sufficient incitement to all Philosophical and Mathematical Heads, to take under serious Consideration the several _Phænomena_, and to endeavour to reconcile them by some general Rule: Yet so it is; that almost all the Authors, from whom a Discourse of this kind ought to have been expected, pass by in silence the Difficulties they here Encounter. And those that mention this Variation: By affirming it to proceed from Causes altogether uncertain (as are the casual lying of Iron Mines and Loadstones in the Earth) put a stop to all further Contemplation; and give discouragement to those that would otherwise undertake this Enquiry. 'Tis true, that not long since one Mr. _Bond_, an old Teacher of Navigation, put forth a small Treatise, wherein he pretends to calculate the Variation: But he limits his Hypothesis to the City of _London_, affirming himself (as he had a great deal of reason) that the same _Calculus_ is not sufficient for other Places; whereby it appears that this Rule is far short of the so much desir'd general one.

Now although (through want of sufficient Observations, and some other Difficulties, which I shall anon shew) I cannot pretend perfectly to establish the Numbers and Rules of a _Calculus_, which shall precisely answer to the Variations of all parts of the World: Yet I suppose it will not be unacceptable to the Curious to propose something of a Light into this abstruse Mystery; which, if no other, may have this good Effect, to stir up the Philosophical _Genii_ of the Age to apply themselves more attentively to this useful Speculation. But before I proceed, 'twill be necessary to lay down the Grounds upon which I raise my Conclusions; and at once to give a Synopsis of those Variations, which I have reason to look upon as sure, being mostly the Observations of Persons of good Skill and Integrity.

A TABLE OF VARIATIONS.

_Names of | _Longitude |_Latitude._| _Anno | _Variation Places._ | from_ Lon.| | Dom._| Observ'd._ | | | | | _d_ _m_ | _d_ _m_ | | _d_ _m_ _London_ | 0 0 | 51 32 N | 1580 | 11 15 E | | | 1622 | 6 0 E | | | 1634 | 4 5 E | | | 1672 | 2 30 W _Paris_ | 2 25 E | 48 51 N | 1683 | 4 30 W | | | 1640 | 3 00 E | | | 1666 | 0 0 | | | 1681 | 2 30 W _Uraniburg_ | 13 0 E | 55 54 N | 1672 | 2 35 W ----------------------------+------------+-----------+-------+------------ _Copenhagen_ | 12 53 E | 55 41 N | 1649 | 1 30 E | | | 1672 | 3 35 W _Dantzick_ | 19 0 E | 54 23 N | 1679 | 7 00 W _Mompelier_ | 4 0 E | 43 37 N | 1674 | 1 10 W _Brest_ | 4 25 W | 48 23 N | 1680 | 1 45 W ----------------------------+------------+-----------+-------+------------ _Rome_ | 13 0 E | 41 50 N | 1681 | 5 0 W _Bayonne_ | 1 20 W | 43 30 N | 1680 | 1 20 W _Hudson's_ Bay | 79 40 W | 51 00 N | 1668 | 19 15 W In _Hud._ Straights | 57 00 W | 61 00 N | 1668 | 29 30 W In _Baffin's_ Bay at } | | | | Sir _Thomas Smith's_} | 80 00 W | 78 00 N | 1616 | 57 00 W Sound } | | | | ----------------------------+------------+-----------+-------+----------- At Sea | 50 0 W | 38 40 N | 1682 | 7 30 W At Sea | 31 30 W | 43 50 N | 1682 | 5 30 W At Sea | 42 0 W | 21 0 N | 1678 | 0 40 E Cape St. _Aug._ of _Brazile_| 35 30 W | 8 0 S | 1670 | 5 30 E Cape _Frio_ | 41 10 W | 22 40 S | 1670 | 12 10 E ----------------------------+------------+-----------+-------+------------ At Sea off of the Mou. } | | | | of the River _Plate_ } | 53 00 W | 39 30 S | 1670 | 20 33 E At the East Entrance } | | | | of _Magellan_ Straits } | 68 00 W | 52 30 S | 1670 | 17 00 E At the W. Entrance of } | | | | the _Magellan_ Straits } | 75 00 W | 53 00 S | 1670 | 14 10 E _Baldivia_ | 73 00 W | 40 00 S | 1670 | 8 10 E ----------------------------+------------+-----------+-------+------------ At Cape d'_Agulbas_ | 16 30 E | 34 50 S | 1622 | 2 00 W | | | 1675 | 8 00 W At Sea | 1 0 E | 34 30 S | 1675 | 0 00 At Sea | 20 0 W | 34 0 S | 1675 | 10 30 E At Sea | 32 0 W | 24 0 S | 1675 | 10 30 E ----------------------------+------------+-----------+-------+------------ At St. _Helena_ | 6 30 W | 16 00 S | 1677 | 0 40 E At _Ascension_ | 14 30 W | 7 50 S | 1678 | 1 00 E At _Johanna_ | 44 00 E | 12 15 S | 1675 | 19 30 W At _Monbasa_ | 40 00 E | 4 00 S | 1675 | 16 00 W At _Zocatra_ | 56 00 E | 12 30 N | 1674 | 17 00 W ----------------------------+------------+-----------+-------+------------ At _Aden_, at the Mo. } | | | | of the _Red Sea_ } | 47 30 E | 13 00 N | 1674 | 15 00 W At _Diego Roiz_ | 61 0 E | 20 0 S | 1676 | 20 30 W At Sea | 64 30 E | 0 0 | 1676 | 15 30 W At Sea | 55 0 E | 27 0 S | 1676 | 24 00 W ----------------------------+------------+-----------+-------+------------ At _Bombay_ | 72 30 E | 19 0 N | 1676 | 12 00 W At Cape _Comorin_ | 76 00 E | 8 15 N | 1680 | 8 48 W At _Ballafore_ | 87 00 E | 21 30 N | 1680 | 8 20 W At Fort St. _George_ | 80 00 E | 13 15 N | 1680 | 8 10 W At the W. Point of _Java_ | 104 00 E | 6 40 S | 1676 | 3 10 W ----------------------------+------------+-----------+-------+------------ At Sea | 58 00 E | 39 0 S | 1677 | 27 30 W At the Isle of St. _Paul_ | 72 0 E | 38 0 S | 1677 | 23 30 W At _Van Dimen's_ Land | 142 0 E | 42 25 S | 1642 | 0 0 At _New Zealand_ | 170 0 E | 40 50 S | 1642 | 9 0 E At _Three Kings Isle_ in } | | | | _New Zealand_. } | 169 30 E | 34 35 S | 1642 | 8 40 E ----------------------------+------------+-----------+-------+------------ At the Isle _Rotterdam_ } | | | | in the South Sea } | 184 00 E | 20 15 S | 1642 | 6 20 E On the Coast of _N. Guin._ | 149 00 E | 4 30 S | 1643 | 8 45 E At the W. P. of _N. Guin._ | 126 00 E | 0 26 S | 1643 | 5 30 E

Tho' I could wish we could obtain from the _Spaniards_ what Variations they find in their Voyages from the _Manilhas_ towards _Acapulco_, through the North part of the South Sea; as likewise what it is at _Japan_ from the _Dutch_: Yet (considering the number of these Observations I have collected, and that they are made in parts of the World so remote from _Europe_, and from one another) I suppose that the Theory that answers these will scarce fail in those Regions from whence we have as yet no account. But first we must make some Remarks upon the foregoing Table: And, First,

That in all _Europe_ the Variation at this time is West, and more in the Eastern Parts thereof than the Western: As likewise, that it seems throughout to be upon the increase that way.

Secondly, That on the Coast of _America_, about _Virginia_, _New-England_ and _New-Foundland_, the Variation is likewise Westerly; and that it increases all the way as you go Northerly along the Coast, so as to be above 20 Degrees at _New-Found-Land_, nearly 30 gr. in _Hudson's Straights_, and not less than 57 Degrees in _Baffin's Bay_; also, that as you Sail Eastward from this Coast, the Variation diminishes. From these two it is a Legitimate Corollary: That _Somewhere between_ Europe, _and the North part of_ America, _there ought to be an Easterly Variation, or at least no Westerly_. And so I conjecture it is about the Eastermost of the _Tercera Islands_.

Thirdly, That on the Coast of _Brasile_ there is East Variation, which increases very notably as you go to the Southward, so as to be 12 Degrees at _Cape Frio_, and over against the River of _Plate_ 20½ Degrees: And from thence Sailing South-Westerly to the Straits of _Magellan_ it decreases 17 Degrees, and at the West Entrance but 14 Degrees.

Fourthly, That at the Eastward of _Brasile_, properly so call'd, this Easterly Variation decreases, so as to be very little at St. _Helena_ and _Ascension_, and to be quite gone, and the Compass Point true about 18 Degrees of Longitude West from the Cape of _Good-hope_.

Fifthly, That to the Eastward of the aforesaid Places a Westward Variation begins, which Reigns in the whole _Indian_ Sea, and arises to no less than Eighteen Degrees under the Equator it self, about the Meridian of the Northern part of _Madagascar_; and near the same Meridian, but in 39 Degrees South Latitude it is found full 27½ Degrees: From thence Easterly the West Variation decreases, so as to be little more than eight Degrees at _Cape Comorin_, and than three Degrees upon the Coast of _Java_; and to be quite extinct about the _Molucca Islands_, as also a little to the Westwards of _Van Diemens_ Land found out by the _Dutch_ in 1642.

Sixthly, That to the Eastward of the _Molucca's_ and _Van Diemens_ Land in South Latitude there arises another Easterly Variation, which seems not so great as the former, nor of so large Extent; for that at the Island _Rotterdam_ it is sensibly less than upon the East Coast of _New Guinea_; and, at the rate it decreases, it may well be suppos'd, that about 20 Degrees farther East, or 225 Degrees East Longitude from _London_, in the Latitude of 20 Degrees South, a Westerly Variation begins.

Seventhly, That the Variations observ'd by the Honourable Sir _John Norborough_ at _Baldivia_, and at the West Entrance of the _Straights_ of _Magellan_ do plainly shew, that That East Variation, noted in our third Remark, is decreasing apace; and that it cannot reasonably extend many Degrees into the South Sea from the Coast of _Peru_ and _Chili_, leaving room for a small Westerly Variation, in that Tract of the unknown World that lies in the mid-way between _Chili_ and _New-Zealand_, and between _Hounds-Island_ and _Peru_.

Eighthly, That in Sailing North-West from St. _Helena_ by _Ascension_, as far as the Equator, the Variation continues very small East, and as it were constantly the same: So that in this part of the World the Course, wherein there is no Variation, is evidently no Meridian, but rather North-West.

Ninthly, That the Entrance of _Hudson's Straights_, and the Mouth of the River of _Plate_, being nearly under the same Meridian, at the one place the Needle varies 29½ Degrees to the _West_; at the other 20½ Degrees to the _East_. This plainly demonstrates the impossibility of reconciling these Variations by the Theory of _Bond_; _which is by two Magnetical Poles and an Axis, inclin'd to the Axis of the Earth_; from whence it would follow, That _under the same Meridian the Variation should be in all places the same way_.

These things being premised may serve as a sure Foundation to raise the Superstructure of a Theory upon. But first it would not be amiss to shew hereby the mistake of _Gilbert_ and _Des Cartes_: The first whereof supposes, that _the Earth it self being in all its parts Magnetical, and the Water not; wheresoever the Land is, thither also should the Needle turn, as to the greater quantity of Magnetical Matter_. But this in many Instances is not true; but most remarkably upon the Coast of _Brazile_, where the Needle is so far from being attracted by the Land, that it turns the quite contrary way, leaving the Meridian to lye N b E, which is just along the Coast. As to the Position of _Des Cartes_, _that the Iron and Loadstones hid in the Bowels of the Earth and the Bottom of the Sea, may be the Causes that the Needle varies_; if we consider for how great a part of the Earths Surface, _ex. gr._ in the whole _Indian_ Sea, the Needle declines the same way, and that regularly, 'twill follow that the attracting Substance that occasions it, must be very far distant. Now by Experience we find the little force that Iron Guns have upon the Compass in Ships (their Vertue, though they be Demiculverin, or greater Cannon, being not perceptible at four or five Yards distance) and the Experiments now before the _Royal Society_ do plainly shew, how little a Magnetism there is in most crude Iron Oars: What quantity thereof must be then suppos'd to make so powerful a Diversion at two or three Thousand Miles distance? Yet I cannot deny that in some places near the Shoar, or in Shoal-Water, the Needle may be irregularly directed from the aforesaid Causes, and that not a little, as _Gassendus_ gives a notable instance of the Island _Elba_ in the Mediterranean Sea: But these differences from the general Direction are always signs of the nearness of those Magnetical Substances, for the Production whereof that Island _Elba_ has been famous from all Antiquity. Besides, against both _Des Cartes_ and _Gilbert_, the change of the Variation, which has been within these Hundred Years last past more than 15 gr. at _London_, is an entire Demonstration; tho' _Des Cartes_ does not stick to say, that the transportation of Iron from place to place, and the growth of new Iron within the Earth, where there was none before, may be the cause thereof. The same holds likewise against the _Hypothesis_ of _Magnetical Fibres_, which _Kircher_ maintains.

Now to propose something that may answer the several appearances, and introduce nothing strange in Philosophy, after a great many close Thoughts, I can come to no other Conclusion than that, _The whole Globe of the Earth is one great Magnet, having four Magnetical Poles, or Points of Attraction, near each Pole of the Equator. Two; and that, in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is govern'd thereby, the nearest Pole being always predominant over the more remote_. The parts of the Earth wherein these Magnetical _Poles_ lie, cannot as yet be exactly determin'd for want of sufficient _Data_ to proceed Geometrically; but, as near as Conjecture can reach, I reckon that the _Pole_, which is at present nearest to us, lies in or near the Meridian of the Lands-end of _England_, and not above seven Degrees from the Pole Arctick; by this _Pole_ the Variations in all _Europe_ and _Tartary_, and the _North Sea_ are principally govern'd, though with regard to the other Northern Pole, whose situation is in a _Meridian_ passing about the middle of _California_, and about 15 gr. from the North Pole of the World; to this the Needle has chiefly respect in all the North _America_, and in the two Oceans on either side thereof, from the _Azores_ Westward to _Japan_, and farther. The two Southern Poles are rather farther distant from the South Pole of the World: The one about sixteen Degrees therefrom, is in a Meridian, some twenty Degrees to the Westward of _Magellan Straights_, or ninety five Degrees West from _London_: This commands the Needle in all the _South-America_, in the _Pacifick Sea_, and the greatest part of the _Ethiopick_ Ocean. The Fourth and last _Pole_ seems to have the greatest Power, and largest Dominions of all, as it is the most remote from the _Pole_ of the World, being little less than 20 Degrees distant therefrom in the Meridian, which passes through _Hollandia Nova_, and the Island _Celebes_ about one hundred and twenty Degrees East from _London_; this Pole is predominant in the South part of _Africa_, in _Arabia_ and the _Red Sea_, in _Persia_, _India_, and its Islands, and all over the _Indian Sea_, from the Cape of _Good-Hope_ Eastwards to the middle of the great South Sea, that divides _Asia_ from _America_. This seems to be the present Disposition of the Magnetical Vertue throughout the whole Globe of the Earth; it remains to shew how this Hypothesis makes out all the Variations that have been observ'd of late; and how it answers to our several Remarks drawn from the Table. And first it is plain, that (our _European_ North _Pole_ being in the Meridian of the Lands-end of _England_) all places more Easterly than that will have it on the West side of their Meridian, and consequently the Needle, respecting it with its Northern Point, will have a Westerly Variation, which will still be greater as you go to the Eastwards, till you come to some Meridian of _Russia_, where 'twill be greatest, and from thence decrease again. Thus at _Brest_ the Variation is but 1¾ Degrees, at _London_ 4½ Degrees; but at _Dantzick_ seven Degrees West. To the Westward of the Meridian of the Lands-end, the Needle ought to have an Easterly Variation; were it not that (by approaching the _American_ Northern _Pole_, which lies on the West side of the Meridian, and seems to be of greater force than this other) the Needle is drawn thereby Westwards, so as to counterballance the Direction given by the _European Pole_, and to make a small West Variation in the Meridian of the Lands-end it self. Yet I suppose that about the Meridian of the Isle _Tercera_, our nearest _Pole_ may so far prevail as to give the Needle a little turn to the East, though but for a very small space: The Counterballance of those two _Poles_ permitting no considerable Variation in all the Eastern Parts of the _Atlantick_ Ocean; nor upon the West Coasts of _England_ and _Ireland_, _France_, _Spain_ and _Barbary_. But to the Westwards of the _Azores_ the Power of the _American_ Pole overcoming that of the _European_, the Needle has chiefly respect thereto, and turns still more and more towards it as you approach it. Whence it comes to pass, that on the Coast of _Virginia_, _New-England_, _New-found-Land_, and in _Hudson's-Straights_ the Variation is Westward; that it decreases as you go from thence towards _Europe_, and that it is less in _Virginia_ and _New-England_, than in _New-found-Land_, and _Hudson's-Straights_. This Westerly Variation again decreases, as you pass over the _North America_; and about the Meridian of the middle of _California_ the Needle again points due North; and from thence Westward to _Yedzo_ and _Japan_, I make no doubt but the Variation is Easterly, and half the Sea over no less than fifteen Degrees, if there be any truth in this Hypothesis of mine. Therefore I propose this as a Trial, that the whole may be scann'd thereby; and I conceive it will not be hard to know of the _Spaniards_ how it is, who so frequently sail through that Ocean, in their return from the _Manilha_ Isles. This East Variation extends over _Japan_, _Yedzo_, _East-Tartary_, and part of _China_, till it meet with the Westerly, which is govern'd by the _European_ North Pole, and which I said was greatest some where in _Russia_.

Towards the Southern Pole the effect is much the same, only that here the South Point of the Needle is attracted. Hence it will follow, that the Variation on the Coast of _Brazile_, at the River of _Plate_, and so on to the Straights of _Magellan_, should be Easterly (as in our third Remark); if we suppose a Magnetical Pole situate about twenty Degrees more Westerly than the Straights of _Magellan_. And this Easterly Variation doth extend Eastward over the greatest part of the _Ethiopick_ Sea, till it be counterpoised by the Vertue of the other Southern _Pole_; as it is about mid-way between the Cape of _Good-Hope_, and the Isles of _Tristan d' Acuntia_. From thence Eastwards, the _Asian_ South Pole (as I must take the liberty to call it) becoming prevalent, and the South point of the Needle being attracted thereby, there arises a West Variation, very great in quantity and extent, because of the great distance of this Magnetical Pole of the World. Hence it is, that in all the _Indian_ Sea as far as _Hollandia Nova_, and farther, there is constantly West Variation; at that under the Equator it self it arises to no less than eighteen Degrees, where 'tis most. About the Meridian of the Island _Celebes_, being likewise that of this Pole, this Westerly Variation ceases, and an Easterly begins; which reaches, according to my Hypothesis, to the middle of the _South-Sea_, between _Zelandia Nova_, and _Chili_, leaving room for a small _West Variation_ govern'd by the _American_ South Pole, which I shew'd to be in the _Pacifick Sea_, in the sixth and seventh Remark.

What I have now said, does plainly shew the sufficiency of this Hypothesis for solving the Variations that are at this time observ'd in the temperate and frigid _Zones_, where the Direction of the Needle chiefly depends upon the Counterpoise of the forces of two Magnetical Poles of the same Nature; and I suppose I have shewn how it comes to pass, that under the same Meridian the Variation should be in one place 29½ West, and another 20½ East; as I have noted in my ninth Remark.

In the _Torrid Zone_, and particularly under the Equinoctial, respect must be had to all four Poles, and their Positions well consider'd, otherwise it will not be easie to determine what the Variations shall be; the nearest _Pole_ being always the strongest; yet not so, as not to be counterballanc'd sometimes by the united forces of two more remote; a notable Instance whereof is in our eighth Remark, where I took notice, that in sailing from St. _Helena_ by the Isle of _Ascension_, to the Equator, on a N. W. Course, the Variation is very little Easterly, and in that whole Tract unalterable; for which I give this Reason, That the South _American_ Pole (which is considerably the nearest in the aforesaid Places) requiring a great Easterly Variation, is counterpoised by the contrary Attraction of the _North-American_ and the _Asian-South-Pole_; each whereof singly are in these Parts, weaker than the _American-South-Pole_; and upon the North West Course, the Distance from this latter is very little varied; and as you recede from the _Asian-South-Pole_, the Ballance is still preserv'd by the access towards the _North-American-Pole_. I mention not in this Case the _European-North-Pole_, its Meridian being little remov'd from those of these places; and of it self requiring the same Variations we here find. After the same manner we might proceed to conclude the Variations in other places under and near the Equator; but I purposely leave it for an Exercise to the Thoughts of the serious Reader, who is desir'd to help his Imagination, by having before him a Map or Globe of the Earth: And to mark thereon the Magnetical _Poles_ in the _Longitudes_ and _Latitudes_ I assign them. (_Vide Plate 2._)

Thus, I hope, I have not lost my Pains and Study in this difficult Subject; believing that I have put it past doubt, _That there are in the Earth four such Magnetical Points or Poles, which occasion the great variety and seeming irregularity which is observed in the Variations of the Compass_. But to calculate exactly what it is, in any place assign'd, is what I dare not yet pretend to, though I could wish it were my happiness to be able to oblige the World with so useful a piece of Knowledge; there are Difficulties that occur, that render the thing as yet not feasible; for first there are a great many Observations requisite, which ought to be made at the same time; not at Sea, but ashore, with greater Care and Attention than the generality of Sailors apply. And besides, it remains undetermin'd in what proportion the attractive Power decreases, as you remove from the _Pole_ of a Magnet, without which it were a vain attempt to go about to calculate. There is yet a further Difficulty, which is the Change of the Variation, one of the Discoveries of this last Century; which shews, that it will require some hundreds of Years to establish a compleat Doctrine of the Magnetical System. From the foregoing Table it should seem, that all the Magnetical _Poles_ had a motion Westward: But if it be so, 'tis evident, that it is not a Rotation about the Axis of the Earth; for then the Variations would continue the same, in the same parallel of _Latitude_ (the _Longitude_ only chang'd) as much as is the motion of the Magnetical _Poles_, but the contrary is found by Experience; for there is no where in the Latitude of 15½ North between _England_ and _America_, a Variation of eleven Degrees East at this time; as it was once here at _London_; it seems therefore, that our _European_ Pole is grown nearer the Pole _Arctick_ than it was heretofore, or else that it has lost part of its Vertue. But whether these Magnetical Poles move altogether with one motion, or with several; whether equally or unequally; whether Circular or Libratory: If Circular, about what Center; if Libratory, after what manner; are Secrets as yet utterly unknown to Mankind, and are reserv'd for the Industry of future Ages.

_An Account of the Cause of the Change of the Variation of the
Magnetical Needle, with an Hypothesis of the Structure of the
Internal Parts of the Earth; as it was proposed to the _Royal
Society_ in one of their late Meetings. By Mr. _Edmund Halley_._

Having in the precedent Discourse delivered a Theory of the Variation of the Magnetical Compass, wherein I did collect as many Observations as at that time I could procure, and having carefully compar'd them together, I came at length to this general conclusion, _That the Globe of the Earth might be supposed to be one great Magnet, having four Magnetical Poles or Points of Attraction, near each Pole of the Equator two; and that in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is chiefly govern'd thereby; the nearest Pole being always predominant ever the more remote_. And I there have endeavour'd to state and limit the present Position of those Poles in the Surface of our Globe, which the Reader pleasing to consult, will save us the pains of repeating. But after all, tho' that Discourse was favourably receiv'd both at home and abroad, as seeming to render a tolerable account of the observ'd Variations, yet I found two Difficulties not easie to surmount; the one was, that no Magnet I had ever seen or heard of, had more than two opposite _Poles_, whereas the Earth had visibly four, and perhaps more. And secondly, it was plain that these _Poles_ were not, at least all of them, fixt in the Earth, but shifted from place to place, as appear'd by the great Changes in the Needles Direction within this last Century of Years, not only at _London_, (where this great Discovery was first made) but almost all over the Globe of Earth; whereas it is not known or observ'd that the _Poles_ of a Load-stone ever shifted their place in the Stone, nor (considering the compact hardness of that Substance) can it easily be suppos'd; though the Matter of Fact be too notorious and universal, not to be accounted for.

These Difficulties had wholly made me despond, and I had long since given over an Inquiry I had so little hopes of, when in accidental Discourse, and least expecting it, I stumbl'd on the following Hypothesis; in delivering whereof, if I shall seem to advance any thing that looks like Extravagant or Romantick, the Reader is desir'd to suspend his Censure, till he have consider'd the force and number of the many Arguments which concur to make good so new and so bold a Supposition.

Though it be sufficiently known and allow'd, that the Needles Variation changes, it will be necessary however to give a few Instances, whereby it may appear that this Change is gradual and universal, and the effect of a great and permanent motion: For which take the following Examples.

At _London_, in the Year 1580, the Variation was observ'd by Mr. _Burrows_ to be 11° 15' East. In _Anno_ 1622, the same was found by Mr. _Gunter_ to be but 6° 0' East. In the Year 1634, Mr. _Gellibrand_ found it 4° 5' East. In 1657, Mr. _Bond_ observ'd that there was no Variation at _London_. _Anno_ 1672, my self observ'd it 2° 30' to the West; and in the Year 1692, I again found it 6° 00' West. So that in 112 Years the Direction of the Needle has chang'd no less than seventeen Degrees.

At _Paris_, _Orontius Finæus_ about the Year 1550, did account it about eight or nine Degrees East Variation. _Anno_ 1640, it was found three Degrees East. _Anno_ 1660, there was no Variation there, and _Anno_ 1681, I found it to be 2° 30' to the West.

At _Cape d' Agulhas_, the most Southerly Promontary of _Africa_, about the Year 1600, the Needle pointed due North and South without Variation, whence the _Portugueze_ gave its name. _Anno_ 1622, there was two Degrees West Variation. _Anno_ 1675, it was 8° 50' West; and in the Year 1691, it was curiously observ'd not less than eleven Degrees West.

At St. _Helena_, about the Year 1600, the Needle declin'd eight Degrees to the East. _Anno_ 1623, it was but 6° 0' East. _Anno_ 1677, when I was there, I observ'd it accurately on Shoar to be 0° 40' East; and in 1692 it was found about 1° to the Westward of the North.

At _Cape Comorine_ in _India_, in the Year 1620, there was 14° 20' West Variation. In the Year 1680, there was 8° 48', but now lately in the Year 1688, it was no more than 7° 30', so that here the Needle has return'd to the East about seven Degrees in seventy Years.

In all the other Examples the Needle has gradually mov'd towards the West, and the places are too far asunder to be influenc'd by the removal of any Magnetical Matter, which may by accident be transplac'd within the Bowels, or on the Surface of the Earth. If more Examples are desir'd, the Reader may be furnished with them in the _Portugueze Routier_ of _Aleixo de Motta_ (written about the Year 1600) and in the Voyage of _Beaulieu_, both publish'd in Mr. _Thevenot_'s first Collection of curious Voyages, Printed at _Paris_, _Anno_ 1663; which he is to compare with the Journals of our late _East India_ Voyagers, and I am assur'd, that it will be thereby evident, that the Direction of the Needle is in no place fix'd and constant, tho' in some it change faster than in others: And where for a long time it has continu'd as it were unalter'd, it is there to be understood, that the Needle has its greatest Deflection, and is become Stationary in order to return, like the Sun, in the Tropick. This, at present, is in the _Indian Sea_, about the Island _Mauritius_, where is the highest West Variation, and in a Tract tending from thence into the N. N. W. towards the _Red-Sea_ and _Egypt_. And in all Places to the Westward of this Tract, all over _Africa_ and the Seas adjoining, the West Variation will be found to have encreas'd; and to the Eastwards thereof as in the Example of _Cape Comorine_, to have decreased, _viz._ all over the _East-Indies_, and the Islands near it.

After the like manner in that Space of East Variation, which, beginning near St. _Helena_, is found all over the South _America_, and which at present is highest about the Mouth of _Rio de la Plata_, it has been observ'd, that in the Eastern Parts thereof, the Variation of the Needle gradually decreases; but whether on the contrary it increases in those places which lie more Westerly than that Tract wherein the highest East Variation is found; or how it may be in the vast _Pacifick Sea_, we have not Experience enough to ascertain, only we may by Analogy infer, that both the East and West Variations therein do gradually increase and decrease after the same Rule.

These _Phænomena_ being well understood and duly consider'd, do sufficiently evince, That the whole Magnetical System is by one, or perhaps more motions translated, whether Eastwards or Westwards, I shall anon discuss; that this moving thing is very great, as extending its effects from Pole to Pole, and that the motion thereof is not _per saltum_, but a gradual and regular motion.

Now considering the Structure of our _Terraqueous_ Globe, it cannot be well suppos'd that a very great part thereof can move within it, without notably changing its Center of Gravity and the Equilibre of its Parts, which would produce very wonderful Effects in changing the Axis of diurnal Rotation, and occasion strange alteration in the Seas Surface, by Inundations and Recesses thereof, such as History never yet mention'd. Besides, the solid parts of the Earth are not to be granted permeably by any other than fluid Substances, of which we know none that are any ways Magnetical. So that the only way to render this motion intelligible and possible, is to suppose it to turn about the Center of the Globe, having its Center of Gravity fix'd and immoveable in the same common Center of the Earth: And there is yet requir'd, that this moving internal Substance be loose and detached from the external Parts of the Earth whereon we live; for otherwise, were it affix'd thereto, the whole must necessarily move together.

So then the External Parts of the Globe may well be reckon'd as the Shell, and the Internal as a _Nucleus_ or inner Globe, included within ours, with a fluid Medium between, which having the same Common Center and Axis of diurnal Rotation, may turn about with our Earth each twenty four Hours; only this outer Sphere having its turbinating motion some small matter either swifter or slower than the internal Ball: And a very minute Difference in length of time, by many Repetitions becoming sensible, the Internal Parts will by degrees recede from the External, and not keeping pace with one another, will appear gradually to move either Eastwards or Westwards by the difference of their motions.

Now supposing such an Internal Sphere having such a motion, we shall solve the two great Difficulties we encounter'd in my former Hypothesis: For if this exteriour Shell of Earth be a Magnet, having its Poles at a distance from the Poles of diurnal Rotation; and if the Internal _Nucleus_ be likewise a Magnet, having its Poles in two other places, distant also from the Axis; and these latter by a gradual and slow motion change their place in respect of the External; we may then give a reasonable account of the four Magnetical Poles I presume to have demonstrated before; as likewise of the Changes of the Needles Variations, which till now hath been unattempted.

The Period of this Motion being wonderful great, and there being hardly an hundred Years since these Variations have been duly observ'd, it will be very hard to bring this Hypothesis to a Calculus, especially since, though the Variations do increase and decrease regularly in the same place, yet in differing places, at no great distance, there are found such casual Changes thereof as can no ways be accounted for by a regular Hypothesis; as depending upon the unequal and irregular distribution of the Magnetical Matter within the Substance of the External Shell or Coat of the Earth, which deflect the Needle from the Position it would acquire from the effect of the general Magnetism of the whole. Of this the Variations at _London_ and _Paris_ give a notable Instance, for the Needle has been constantly about 1°½ more Easterly at _Paris_ than at _London_; though it be certain that according to the general effect, the Difference ought to be the contrary way: Notwithstanding which, the Variations in both places do change alike.

Hence, and from some other of like Nature, I conclude, That the two Poles of the External Globe are fixt in the Earth, and that if the Needle were wholly govern'd by them, the Variations thereof would be always the same, with some little Irregularities upon the account I but just now mention'd: But the Internal Sphere having such a gradual translation of its Poles, does influence the Needle, and direct it variously, according to the result of the attractive or directive Power of each Pole; and consequently there must be a Period of the Revolution of this Internal Ball, after which the Variations will return again as before. But if it shall in future Ages be observ'd otherwise, we must then conclude that there are more of these Internal Spheres, and more Magnetical Poles than Four, which at present we have not a sufficient number of Observations to determine, and particularly in that vast _Mar del Zur_, which occupies so great a part of the whole Surface of the Earth.

If then two of the Poles be fixt and two moveable, it remains to ascertain which they are that keep their place; and though I could wish we had the Experience of another Century of Years to found our Conclusions upon, yet I think we may safely determine, That our _European North Pole_ (which in the precedent Discourse I suppos'd near the Meridian of the Lands-end of _England_, and about seven Degrees therefrom) is that That is moveable of the two Northern Poles, and that That has chiefly influenc'd the Variations in these parts of the World: For in _Hudson_'s Bay, which is under the Direction of the _American_ Pole, the Change is not observ'd to be near so fast as in these parts of _Europe_, though that Pole be much farther remov'd from the Axis.

As to the South Poles, I take the _Asian_ Pole, which I place about the Meridian of the Island _Celebes_ to be the fixt, and consequently the _American_ Pole to move; from the like Observation of the slow Decrease of the Variation on the Coast of _Java_, and near the Meridian of the _Asian_ Pole; though I must confess to have no account of the effects of the other beyond _Magellan_'s Streights.

If this be allow'd me, 'tis plain that the fixt Poles are the Poles of this External Shell or Cortex of the _Earth_, and the other two the Poles of a Magnetical _Nucleus_ included and moveable within the other. It likewise follows, that this Motion is Westwards, and by consequence that the aforesaid _Nucleus_ has not precisely attained the same degree of Velocity with the exteriour Parts in their diurnal Revolution; but so very nearly equals it, that in 365 Revolves the difference is scarce sensible. This I conceive to arise from the Impulse whereby this diurnal Motion was imprest on the Earth, being given to the External Parts, and from thence in time communicated to the Internal; but not so as perfectly to equal the Velocity of the first Motion impress'd on, and still conserv'd by the superficial Parts of the Globe.