Digitale Ausgabe

The calculation is as follows:—I suppose that the point B(fig. 3.) is the north magnetic pole of the earth, and thatthe point A is the south magnetic pole: I suppose also thatthere is in the point M, at the surface of the earth, a mo-lecula of the austral fluid which is attracted by B and re-pelled by A in the inverse ratio of the square of the di-stance; and I require what will be the direction of thepower resulting from these two forces acting on that mole-cula. It is evident that this direction will be that alsowhich would be assumed in the point M by the needle ofa compass freely suspended: for, in consequence of thesmallness of the needle in comparison of the radius of theearth, the lines drawn from its points to one centre, B or A,may be considered as parallel, especially if the points Aand B are near the centre of the earth; which is the casewith nature, as may be seen. I shall first suppose that the earth has a spherical figure,and that the two poles A and B are equal in force; I shallthen examine how far the latter supposition agrees with theresults observed. Let AM then = D′, BM = D, CP = x; PM = y,the angle MCP = u, CA = CB = a, and I shall make a = Kr; r being equal to the radius of the earth, and K aconstant but indeterminate quantity. Let X, Y, also be the forces which attract M in a direc-tion parallel to the axes of the co-ordinates, and β the anglewhich the resulting force makes with the axis ABC. We shall first have the following equations, in whichF is the magnetic force, at a distance equal to unity.

• \( \text{X}=\frac{\text{F}}{\text{D}^2}\;\text{cos. M B D}-\frac{\text{F}}{\text{D}'^{2}}\text{ cos. M A D} \);
• \( \text{D}'^2=y^2+(x+a)^2=r^2+2\;\text{axis}\;+a^2 \)
• \( \text{Y}=\frac{\text{F}}{\text{D}^2}\;\text{sin. M B D}\;-\frac{\text{F}}{\text{D}'^2}\;\text{sin. M A D} \);
• \( \text{D}^2=y^2+(x-a)^2=r^2-2\;\text{axis}\;+a^2 \),

|300| or by putting for the cosines their values:

• \( \text{X}=\frac{\text{F}(x-a)}{\text{D}^3}-\frac{\text{F}(x+a)}{\text{D}'^{\text{3}}} \)
• \( \text{Y}=\frac{\text{F}y}{\text{D}^{\text{3}}}-\frac{\text{F}y}{\text{D}'^{\text{3}}} \);

and as we have

• \( \text{tang.}\;\beta =\frac{Y}{X} \),

we shall have also

• \( \text{tang.}\;\beta=\frac{{\frac{y}{\text{D}^3}-\frac{y}{\text{D}'^3}}}{{\frac{x-a}{\text{D}^3}-\frac{x-a}{\text{D}'^3}}}=\frac{{y(\text{D}'^3-\text{D}^3)}}{{x(\text{D}'^3-\text{D}^3)-a\text{(D}'^3\text{+D}^3)}} \);

and putting for x, y, and a, their values, r cos. u; r sin. u;Kr;

• \( \text{tang.}\;\beta=\frac{{\text{sin.}\;u}}{\text{cos.}\;u-\text{K}\left(\frac{\text{D}'^3+\text{D}^3}{\text{D}'^3-\text{D}^3}\right)} \);
• \( \text{D}'^2=r^2(1+2\;\text{K cos.}\;u+\;\text{K}^2) \);
• \( \text{D}^2=r^2(1-2\;\text{K cos.}\;u+\;\text{K}^2) \);
• which gives the system of the two equations,
• \( \text{tang.}\;\beta=\frac{{\text{sin.}\;u}}{{\text{cos.}\;u-\text{K}\left(\frac{\text{D}'^3+\text{D}^3}{\text{D}'^3-\text{D}^3}\right)}} \)
• \( \text{K}\left(\frac{{\text{D}'^3+\text{D}^3}}{{\text{D}'^3-\text{D}^3}} \right )=\frac{{{(1+2\text{K cos.}}\;u+\text{K}^2)^\frac{3}{2}+{(1-2\text{K cos.}}\;u+\text{K}^2)^\frac{3}{2}}}{{(1 + 2\text{K cos.}\;u+\text{K}^2)^\frac{3}{2}-(1-2\text{K cos.}\;u+\text{K}})^\frac{3}{2}}\text{K} \).

These equations determine the direction of the magneticneedle in regard to each point M, the distance of whichfrom the magnetic equator is known; but it is seen thatthis direction depends on the quantity K, which representsthe distance of the magnetic centres from the centre of theearth: this distance being expressed in parts of the terres-trial radius, we must therefore first determine this quantityfrom observations. To do it in the manner of approximation, and thus ac-quire a first idea of the value of K, I have chosen an obser-vation made by M. Humboldt at Carichana in 7·2978° (6°34′ 5″) of north latitude counted from the terrestrial equa-tor, and 78·111° (70° 18′) west longitude reckoned from |301| the meridian of Paris; which gives 16·526° (14° 52′ 25″)of latitude counted from the magnetic equator, and 53·7390°(48° 21′ 53″) of west longitude proceeding from the nodeformed by that equator with the equator of the earth. Theinclination of the magnetic needle was observed in thatplace by M. Humboldt in the month of Messidor, year 8,and found to be equal to 33·78° of the centigrade division*.A comparison of this result, with the other observationsof M. Humboldt, shows that it may be indeed consideredas agreeing to that latitude. To make use of it I have successively given to K differentvalues in the formula: I have calculated the inclinationsresulting from that latitude; and, comparing these resultswith that which M. Humboldt really observed, the progressof the errors naturally led me to the most proper supposi-tion. The following is a table of these trials:

Values of K.	Inclinations of the Needle.	Errors.
K＝1	7·73°	26·04°
K＝0·6	18·80	14·97
K＝0·5	22·04	11·73
K＝0·2	29·38	4·39
K＝0·1	30·64	3·13
K＝0·01	31·04	2·73
K＝0·001	31·07	2·7

The first value of K would place the centre of the mag-netic forces at the surface of the earth and the poles of the magnetic equator. It is seen that this supposition cannotbe admitted, because it would give an increase of inclina-tion much less rapid than that indicated by observations.The case is the same with the following results, whichplace the centres of action on the terrestrial radius atdifferent distances from the centre of the earth: but it isseen also, in general, that they approach more and more tothe truth in proportion as this distance becomes less; whichevidently shows that the two centres of action of the mag-netic forces are situated near the centre of the earth. Allthe other observations of M. Humboldt would also lead tothe same consequence. The most proper supposition would be to make K null,or so small that it would be needless to pay attention to it;which amounts to the same thing as to consider the twocentres of action placed, as we may say, in the same mo-lecula. The result, indeed, obtained in this manner is themost exact of all; it is equal to 31·0843°: this value is still

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* All the measures of inclination which I have given in this memoir willbe expressed, like those of M. Humboldt, in decimal parts of a quadrant.|302| a little less than that which M. Humboldt observed, andthe difference is equal to 2·69; but it must be consideredalso that the formula from which we derive these valuessupposes the position of the magnetic equator to be per-fectly determined; but it may not be so with the utmostexactness, according to the only two observations of Lapey-rouse and Humboldt, which we have employed. It is there-fore by studying the progress of the formula, and comparingit with the observations, that we are able to appreciate itjustly; after which we may think of remedying the smallerrors with which it may be accompanied. To obtain the result I have here mentioned, and whichis, as it were, the limit of all those which may be obtainedby giving to K different values, it is to be remarked thatthe quantity

• \( \text{K}\left(\frac{\text{D}'^3+\text{D}^3}{\text{D}'^3-\text{D}^3}\right) \)
• or
• \( \text{K}\frac{(1 + 2\;\text{K cos.}\;u+\text{K}^2)^\frac{3}{2}+(1-2\;\text{K cos.}\;u+\text{K}^2)^\frac{3}{2}}{(1+2\;\text{K cos.}\;u+\text{K}^2)^\frac{3}{2}-(1 - 2\;\text{K cos.}\;u+\text{K}^2)^\frac{3}{2}} \)

becomes \( \frac{0}{0} \) when K is null, but by applying to it themethods of known quantities it will be found that its valuein this supposition is really determinate and equal to \( \frac{1}{3\;\text{cos.}\;u} \).By substituting this in the formula we shall have

• \( \text{tang.}\;\beta=\frac{\text{sin.}\;u}{{{\text{cos.}}\;u-\frac{1}{3\;\text{cos.}\;u}}} \)

an equation which may be reduced to this form:

• \( \text{tang.}\;\beta=\frac{{\text{sin.}\;2u}}{{\text{cos.}\;2u+\frac{1}{3}}} \);

which will easily give the value of β: and when this valueis known we shall have the inclination I, by the followingformula:

• \( \text{I} = 100+u-\beta \),

which will serve throughout the whole extent of the twohemispheres. From the progress I have traced out it is seen that thepreceding formula is not merely an empyric construction ofobservations; on the contrary, it is totally independent, andonly supposes the inclination of the magnetic needle to be |303| produced by a magnet, infinitely small, placed in the centreof the terrestrial surface; but by calculating from this for-mula the inclination for the different latitudes, I have foundprecisely the same numbers as M. Humboldt observed eitherin Europe or in America: and it is not his observations onlythat are represented in this manner; but those which havebeen made in Russia, and at Kola in Lapland, during thelast transit of Venus, are also comprehended under the samelaw. This is proved by the table annexed to this memoir,in which I have calculated the observations of Mallet and Pictet, with a part of those of M. Humboldt, which I tookat random, but, however, in such a manner as to include allthe rest in the intervals. It is seen that the results of the formula deviate very littlefrom the observations; but these differences may be renderedstill smaller. By examining, indeed, the progress of theerrors, it is seen that the numbers given by calculation are alittle too small in America for the low latitudes, and a littletoo great for the high latitudes; which shows that the wholemay be allowed, with some slight modifications, either bychanging, however little, the node and inclination of the magnetic equator, which two observations cannot determinewith the utmost exactness, or by displacing ever so littleour small magnet, leaving, however, its centre in the planeof the magnetic equator, and placing it in such a mannerthat it shall be a little nearer America than Europe. It isby the observations themselves, when we shall have a greaternumber, that we must be guided in these small correc-tions. In a word, it must not be expected that we can representin a rigorous manner, by a mathematical law, all the in-clinations observed; for the phænomenon of the inclination,though more regular than the other magnetic effects, is notfree from some anomalies: this may be easily seen on con-structing the curve given by the observations themselves.Thus, for example, the inclination observed at Popayan is0° 10′ greater than at St. Carlos del Rio Negro, thoughthe magnetic latitude of the latter is 0·6852° (3° 7′) greater.The case is the same with observations made at Javita andSanta-Fé. Other anomalies are discovered in the compara-tive progress of the observations and formula. This is thecase in regard to Carichana, St. Thomas de la Guyane, andCarthagena. The increase of the inclination from the firstto the second of these points is by no means in harmonywith the increase from the second to the third; and if we |304| compare together the intensities observed in these dif-ferent places, the anomalies they exhibit announce insome measure those which the inclination ought to ex-perience. The cause of these anomalies becomes evident from whathas been already remarked; they are merely the effect oflocal circumstances, and arise from the small systems ofattraction by which the general phænomena are modified.This must be sensible in particular for that part of America which M. Humboldt travelled over, and which is traversedthroughout its whole length by the grand chain of the cor-dillera of the Andes. It is also in these places that themost considerable differences exist. Popayan, for example,is situated near the volcanoes of Sotara and Pourace; it isjoined to basaltic mountains abounding with magnetic iron.Near Sulumito, to the east of Popayan, these basaltic co-lumns have very striking poles: in like manner Mexico issituated at the height of 1160 toises on the ridge of thegrand cordillera of Lenschtitlan: the ground there is co-vered with porous basaltes and amygdaloids, which arealmost all charged with magnetic iron. Must not all thesecauses have a sensible influence on the inclination of themagnetic needle; and must not the different dispositions ofthe ferruginous masses, or their change of state, in conse-quence of the action of nature, produce also variations?M. Humboldt made on this point a decisive observation:the earthquake of the 4th of November 1799 changed atCumana the inclination of the needle. On the 1st of No-vember it was 43° 65′; on the 7th it was only 42° 75′; andten months after it returned to 42° 85′: but it did not re-gain its former value; the intensity of the magnetic forcewas not changed by the effect of this earthquake. It is proved, then, by these observations, that local cir-cumstances may have on the inclination a sensible influ-ence; and this influence is remarked in the countries tra-versed by M. Humboldt *. It appears, therefore, that the mathematical hypothesiswhich we have employed really expresses the law of natureat least to the north of the magnetic equator; for, though thefirst results observed towards the south seem to bend to it also,the uncertainty under which we are in regard to the truecause of these phænomena must stop our conjectures, and

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* We can observe that the anomalies are sensible in particular in theislands.—Note by the Authors of the Memoir. |305| prevent us from extending too far the consequences of thelaws which we observe*. From the preceding results, we may calculate the pointswhere the axis of the magnetic equator pierces the terres-trial surface; for their latitudes are equal to the comple-ments of the obliquity of that equator, and their meridian isat 100° of longitude from its nodes. The north magneticpole is found also at 97·7975° (79° 1′ 4″) of north latitude,and at 33·3719° (30° 2′ 5″) of longitude west from Paris,which places it to the north of America. The other mag-netic pole, symmetric to the preceding, is situated in thesame latitude south, and at 66·6281° (149° 67′ 55″) of lon-gitude east from Paris, which places it amidst the eternalice: indications entirely analogous to those of Wilke and Lemonnier. If we could reach these poles, the compass would be seenvertical; but if any confidence can be placed in the lawwhich we have discovered, this would be the only differencewhich would be observed in regard to the inclination, andwe should be still as far distant as in Europe from the realcentres which produce it. This result might appear to beof such a nature as to diminish the interest one might havein visiting these horrid regions, had we not also the hope ofdiscovering there new phænomena in regard to the inten-sity of the magnetic force, and the influence of meteors. These consequences do not entirely accord with theopinion pretty generally received, and which ascribes theincrease of the magnetic effects towards the north to thegreat quantity of iron dispersed throughout these regions;but it appears to us that this opinion is not agreeable to thetruth. The cordillera of the Andes contains an enormousquantity of magnetic iron: the native iron of Chaco, thatproblematic mass analogous to that of Pallas, and those ofXacateras in Mexico, is found even under the tropics†.

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* Since this memoir was read, we can advance something more positive.Observations made at the Cape of Good Hope, Cape Horn, and New Hol-land, by different navigators, are very exactly represented by our formula;and it follows, that it extends also to the austral hemisphere. We hopesoon to have numerous and very exact observations on the inclination ofthe needle in that part of the earth. But we have thought it our duty toadd to our table such results as relate to it, and which we have been ableto procure. We have inserted also two observations on the intensity, madewith great care by M. Rossel, during the expedition of d’Entrecasteaux, whichare very important, as they prove that the terrestrial magnetic force in-creases also in the austral hemisphere in proportion as one removes from the equator.—Note by the Authors of the Memoir. † We may now add to the preceding considerations this decisive fact, thatthe intensity also increases when one approaches the south pole.—Note bythe Authors of the Memoir. |306| On seeing the inclinations of the compass so exactly re-presented in our hypothesis, we endeavoured to discoverwhether it could he applied also to the intensities observedby M. Humboldt; but we found that it did not apply. Itgives, indeed, an increase of the magnetic forces fromthe equator to the pole; but this increase, which at firstis too slow, becomes afterwards too rapid: I have not yetbeen able to try whether the small displacement of the ter-restrial magnet will contribute towards representing thembetter: but it must be remarked, that the series of the in-tensities is extremely whimsical, and contains an infinitenumber of anomalies; so that local phænomena may haveon this phænomenon a much more sensible influence thanon the inclination. On reviewing the results which we have given in thismemoir, it is seen that we have first determined the posi-tion of the magnetic equator by direct observations, whichhad never been done before; we have then proved that themagnetic force increases in proceeding from that equator tothe poles: in the last place, we have given a mathematicalhypothesis, which when reduced to a formula satisfies all theinclinations hitherto observed. Supposing, as we have done in this formula, the smallcorrections of which it is susceptible, its utility becomesevident, either for making known, in the course of time, thevariations which may take place in the action of the terres-trial magnetism, or to ascertain or even foresee the value ofthe inclination, which in a great many cases is of great im-portance. For example, near the magnetic equator, the increase ordiminution of the inclination will indicate to a vessel on avoyage whether she has gained or lost in latitude by cur-rents. This knowledge of the latitude is sometimes as im-portant as that of longitude. On the coasts of Peru, forexample, the currents tend from Chiloé to the north andnorth-east with such force, that one may go from Lima toGuayaquil in three or four days, and two, three, and some-times five months are necessary to return. It is conse-quently of the greatest importance for vessels coming fromChili which stretch along the coast of Peru, to know theirlatitude. If they go beyond the port to which they arebound they must work to the southward, and every day’sprogress requires often a month of return. Unfortunately,the fogs which prevail during four or five months on thecoasts of Peru prevent navigators from distinguishing theform of the coast: nothing is seen but the summits of the |307| Andes, and that of the peaks which rise above that stratumof vapours; but the figure of it is so uniform that pilotsfall into mistakes. They often remain twelve or fifteen dayswithout seeing the sun or the stars, and during that intervalthey come to anchor, being afraid of overshooting their port:but if we suppose that the inclination of the magneticneedle in the ports to the south of Lima is known, forexample at Chancay, Huaura, and Santa, the dipping needlewill show whether it be, in regard to Lima, to the south orthe north. It will show at the same time opposite whatpoint of the coast a vessel is; and this indication will beattended with more exactness than one could hope for, be-cause in these seas the inclination varies with extraordinaryrapidity. M. Humboldt, to whom we are indebted forthese remarks, observed in these seas the following values:

Places.		South Latitudes.		Inclinations.
Huancey	‒	10° 4′	‒	6,80°
Huaura	‒	11 3	‒	9,00
Chancay	‒	11 33	‒	10,35

These observations prove that the error of three or fourdegrees in the inclination in these seas would produce but adegree of error in latitude; and, on account of the tranquil-lity of the Pacific Ocean, the inclination may be observedto within a degree nearly. Frequent instances of such re-sults may be seen in books of voyages. In like manner, ifone knew exactly the inclination at the mouth of the Rio dela Plata, it would be very useful to navigators, who, whenthe Pamperos blow, remain fifteen or eighteen days withoutseeing the heavenly bodies, and go on different tacks forfear of losing the parallel of the mouth of that river. In a word, the inclination may indicate also the longi-tude in these seas: and this method may be employed whenothers fail. A vessel which sails there in the direction ofa parallel could not find its longitude either by a chrono-meter or the declination of Halley, unless a star could beseen in order to take an horary angle or the magnetic azi-muth. The dipping needle, then, throws light on the lon-gitude amidst the thickest fogs. We point out this methodas one of those which have only a local application; buthitherto little attention has been paid to it. These ideasmay be extended and rectified by able navigators. In general, if the inclination of the needle, and the lawwe have tried to establish, could be depended on, to observethe inclination and the terrestrial latitude would be suffi-cient to determine also the longitude: but we have not yetexamined the extent of the errors of which this method may |308| be susceptible, and consequently we confine ourselves to amere indication of it. The phænomenon of the inclination has in maritime ob-servations a particular and very remarkable advantage,namely, that of not being subject to those great progressivevariations which affect the declination. Without repeatingwhat we have already said above on the supposed constancyof this phænomenon, it may be remarked that our formulaeven affords a new proof that it may comprehend in thesame law the observations made thirty-six years ago inLapland, those which Lacaille brought back in 1751 fromthe Cape of Good Hope, and those which M. Humboldt has lately made in America. In short, when we tried to represent the inclinations indifferent latitudes by the supposition of a magnet infinitelysmall, very near the centre of the earth and perpendicularto the magnetic equator, we did not pretend to considerthat hypothesis as any thing real, but only as a mathema-tical abstraction useful to connect the results, and proper toascertain in future whether any changes exist. In regardto the declination and intensity, we freely confess that weare entirely unacquainted with their laws or their causes;and if any philosopher is so fortunate as to bring them toone principle, which explains at the same time the varia-tions of the inclination, it will no doubt be one of thegreatest discoveries ever made. But this research, exceed-ingly difficult, requires perhaps before it be attempted moreobservations, and in particular more precise observationsthan have hitherto been collected. For this reason wethought we might present to the class the preceding re-searches, imperfect as they are, begging it to receive themwith indulgence. Should we be so happy as to find thatour results appear of any utility, we propose to unite all theexact observations which have been made on this subject,in order to give the utmost degree of precision to the lawwe have discovered. |To face Page 308| [To face Page 308.

NORTHERN MAGNETIC HEMISPHERE.

Names of theObservers.	Places ofObservation.	Latitudes reck-oned from the TerrestrialEquator.	Longitudesreckoned fromthe Meridianof Paris.	Latitudes reck-oned from the MagneticEquator.	East Longitudesreckoned fromthe Node of the Magnetic Equa-tor in the SouthSea.	Numberof Oscilla-tions in 10′of Time.	Inclinationsgiven by Theory	Inclinationsgiven by directObservation.	Differences inDegrees of theCentesimalDivision.
		Old Division.	Old Division.	Old Division.	Old Division.		Centig. Division.	Centig. Division.
Humboldt ‒	Magnetic equator in Peru ‒ ‒ ‒	7° 1′ 0″ S	80° 41′ 0″ W	0° 0′ 0″	40° 17′ 56″	211	0,000	0,00	0,00°
Lapeyrouse	Magnetic equator at sea betweenBrazil and the Island of Ascen-sion ‒ ‒ ‒ ‒	10 57 0	25 25 0	0 0 0	95 33 56	‒ ‒ ‒	0,000	0,00	0,00
Humboldt ‒	Tompenda ‒ ‒	5 31 4	80 27 0	1 30 54	39 52 51	213	3,3642	3,55	0,1858
The same ‒	Loxa ‒ ‒ ‒ ‒	4 0 0	81 12 0	2 54 27	38 55 0	212	6,440	6,00	+ 0,44
The same ‒	Cuença ‒ ‒ ‒	2 54 9	80 43 0	4 3 44	39 13 52	214	8,97	9,35	— 0,38
The same ‒	Quito ‒ ‒ ‒ ‒	3 13 17	80 15 0	6 46 59	39 17 52	218	14,87	14,85	+ 0,02
The same ‒	St. Antonio ‒ ‒	0 0 0	80 12 0	7 0 53	39 18 52	220	15,29	16,02	— 0,73
The same ‒	Popayan ‒ ‒ ‒	2 24 33 N	78 45 0	9 36 16	40 24 27	223	‒ ‒ ‒ ‒	23,20	‒ ‒ ‒ ‒
The same ‒	St. Carlos del RioNegro ‒ ‒ ‒	1 52 4	70 10 0	10 13 14	49 6 35	216	22,0278	23,10	— 1,0722
The same ‒	Javita ‒ ‒ ‒ ‒	2 49 0	70 30 0	11 7 40	48 39 6	218	23,87	27,00	— 3,13
The same ‒	Esmeralda ‒ ‒	3 13 26	68 38 0	11 45 45	50 29 15	217	‒ ‒ ‒ ‒	28,85	‒ ‒ ‒ ‒
The same ‒	Santa Fe di Bagota	4 36 5	76 37 0	12 5 13	42 17 13	226	25,76	26,97	— 1,21
The same ‒	Carichana ‒ ‒	6 34 5	70 18 0	14 52 25	48 21 53	227	31,08	33,77	— 2,69
The same ‒	St. Thomas ofGuyana ‒ ‒	8 8 24	66 26 0	16 54 18	52 7 26	222	34,77	39,00	— 4,23
The same ‒	Carthagena ‒ ‒	10 25 57	78 2 0	17 38 43	39 55 13	240	36,07	39,17	— 3,10
The same ‒	Mexico ‒ ‒ ‒	19 26 2	101 22 0	22 35 14	14 36 41	242	44,87	46,85	— 1,98
De Rossel in1791 Humboldt in1799	St. Croix in Tene-riffe ‒ ‒ ‒ ‒	28 28 30	18 37 0	39 12 40	72 0 26	238	64,9975	69,85	— 4,35
The same ‒	Atlantic Ocean ‒	38 52 0	16 20 0	49 28 22	106 30 10	242	74,29	75,76	— 1,47
The same ‒	Paris ‒ ‒ ‒ ‒	48 50 15	0 0 0	57 57 0	128 22 47	245	80,69	77,62	+ 3,07
Euler junior	Petersburgh in1755 ‒ ‒ ‒	59 56 23	27 58 0 E	64 41 0	173 30 25	‒ ‒ ‒	85,21	81,67	+ 3,54
Mallet ‒ ‒	Kola, in Lapland,in 1769 ‒ ‒	68 52 30	30 40 30 E	71 44 36	179 9 29	‒ ‒ ‒	89,59	86,39	+ 3,20
Lord Mul-grave	In an island nearSpitzbergen in1773 ‒ ‒ ‒	79 50 00	7 38 00 E	83 9 50	127 40 5	‒ ‒ ‒	96,1882	91,1111	+ 5,0771

SOUTHERN MAGNETIC HEMISPHERE.

Names of theObservers.	Places ofObservation.	Latitudes reck-oned from the TerrestrialEquator.	Longitudesreckoned fromthe Meridianof Paris.	South Latitudesreckoned fromthe MagneticEquator.	East Longitudesreckoned fromthe Node of the Magnetic Equa-tor in the SouthSea.	Inclinationsgiven by Theory	Inclinationsgiven by directObservation.	Differences inDegrees of theCentesimalDivision.	Number ofOscillationsin 10′ ofTime.
		Old Division.	Old Division.	Old Division.	Old Division.	Centig. Division.	Centig. Division.
Humboldt ‒	Lima ‒ ‒ ‒	12° 2′ 31″ S	79° 33′ 0″ W	4° 48′ 36″ S	41° 42′ 51″	10,6145	11,10	0,4855°	219
Derossel, ex-pedition of Entrecasteaux	Sourabaya in theIsle of Java ‒	7 14 23	110 21 28 E	15 37 22	228 56 50	32,4660	28,5185	+ 3,9475	204
Bayli in 1775	Cape of Good Hope	33 55 30	16 10 0 E	26 15 34	131 38 53	49,58	47,78	+ 1,8	‒ ‒ ‒
Lapeyrouse	Bay of Talcaguara	36 42 0	75 53 0 W	28 42 14	49 0 5	52,8889	55,555	— 2,6667	‒ ‒ ‒
The same ‒	In sight of the Isleof Patagonians	52 21 26	69 38 0 W	44 30 3	57 13 52	70,04	68,89	+ 1,15	‒ ‒ ‒
Derossel, ex-pedition of Entrecasteaux	New Holland ‒	43 34 30	144 36 33 W	54 12 43	263 21 18	78,7037	77,9667	— 0,737	265

The results comprehended in this table extend from 38° 55′ to 263° 21′ 18″ east longitude, reckoned from the node of the magnetic equator in the South Sea:consequently, they comprehend more than 224°, and their agreement shows that in this extent the magnetic equator is sensibly a great circle of the earth. We havenot yet calculated the observations for the 36 degrees of longitude which would complete the contour of that equator.—For the southern hemisphere we have giventhe observations, made with great care, by M. Derossel, during the expedition of d’Entrecasteaux. It results from them that the intensity of the terrestrial magnetismincreases also in that hemisphere, when one removes from the magnetic equator. The inclination observed by M. Derossel at Teneriffe being exactly the same as thatobserved by M. Humboldt eight years after, this agreement has allowed us to render comparable the results obtained by these philosophers in regard to the intensity:for this purpose we have multiplied the results of M. Derossel, by giving the numbers which he and M. Humboldt observed at Teneriffe. The result of this calcula-tion will be found in the column of oscillations. It is there again seen that this phænomenon is very much modified by local circumstances, and incomparably morethan the inclination. The increase of the intensity deduced from the observations of M. Humboldt is less than that which would result from our hypothesis; andthat given by the observations of M. Derossel is too great: which proves that nothing can be determined in regard to the law of this increase. The influence oflocal circumstances on the inclination is particularly sensible in the isles. The declination and intensity of the magnetic forces experience there also sensible anoma-lies. This fact is indicated by several observations, and in particular by those which M. Derossel made at Sourabaya in the Island of Java. In a word, by comparingthe results of our formula with the observations of different navigators, the latter must be examined with critical accuracy, and must not be admitted but whenthey agree with each other and with those of other navigators: without this precaution we should every moment fall into great errors, occasioned by the inco-herency of the results: besides, we present the preceding only as a first approximation.