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It will be recalled that we found that the main distribution phenomena could be represented by two rectangular magnetic systems, a polar and an approximately equatorial, the former of about 5 or 6 times the strength of the latter. This conclusion was reached with the aid of the magnetic observations for 1885. Suppose we carry out the same investigation for other dates, shall we reach the same result?

Let us begin with the year 1780, since for this date we possess the earliest fairly reliable isoclinic chart. This chart gives us the approximate distribution of the magnetic dip for that date. It was constructed by Christopher Hansteen.* The first thing to be done is to construct the "isapoclinics" according to the method explained in No. II. For this purpose, I have scaled the dips for points 20° distant in longitude and in latitudes +60°, ±40°, ±20° and 0°. The data for latitude 60° S. could not be safely obtained and hence the "isapoclinics are not extended beyond 40° S. For the regions of the two foci (secondary dip poles), I have made a few closer scalings.

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Having obtained the data as based upon observation, the computed dip I, is again derived with the aid of equation:

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o being the geographical latitude. It will be remembered that this is the dip that would prevail at the place where the latitude is if the earth were uniformly magnetized about the geographical axis and were at rest. The departure of the actual (or observed) dip from this computed dip is:

^ I = Iobs'd — Icomp'd = I。 — Ie.

These differences we form for all the scaled values, plot them on a map in their true geographical position, and finally draw lines through all the places having the same I, or departure, paying due regard to sign. The lines obtained thus I have termed lines of equal-departing dip or, briefly, isapoclinics. The result for 1780 is given on the diagram, page 316. For the sake of convenience in comparison the same curves for 1885 are reproduced from No. II.+

It will be seen that the main result is the same for both dates. The secondary polarization is again nearly equatorial. Hence, the final conclusion of No. II is borne out by this early date. We shall see later that this is also true for an intermediate year, 1829.

*The chart will be found in the Atlas to his "Untersuchungen über den Magnetismus der Erde, Christiania, 1819. A reduced copy is given in Neumayer's "Atlas des Erdmagnetismus," Gotha, 1891, plate No. 41.

In the reproduction the isapoclinic + 25 has been slightly improved.

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The plus isapoclinics are again simpler in form than the minus ones, and from this fact one could argue that if we were to construct the "equiabspotentials," the foci of the plus equal-departing potentials would fall more closely together with that of the plus isapoclinics, than the one of the minus equiabspotentials with that of the minus isapoclinics.* In other words, in the Indian and Pacific Oceans another disturbing factor seems to come into play. I reached the same conclusion when investigating the secular motion of a free magnetic needle. I found, namely, that the secular magnetic wave travels in the main westward, but in eastern Asia, in the Pacific Ocean and on the western coast of America we have evidences of a wave, seemingly of a smaller amplitude, that travels eastward. We are thus succeeding in gradually drawing the lines closer and closer around the disturbing factors of terrestrial magnetism. And this is very important since theory cannot determine the deflecting centers for us; observation must point them out to us.

The next thing to which I wish to draw attention is the question at the head of this paper-what is the secular motion of the secondary magnetic poles? By comparing both diagrams it will be seen that beyond a doubt the whole secondary magnetic system has been moving along the equator westwardly from 1780 to 1885.

To make this clearer the following figurest are given:

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The assignment of the positions of the poles is liable to an uncertainty of about 5° in latitude and in longitude. It is especially interesting to include in the comparison the results for 1829 as they have been derived from Erman and Petersen's figures based upon the Gaussian potential theory of terrestrial magnetism.

*See footnote to No. II, p. 200.

See "Beitraege zur Kenntniss des Wesens der Saecular-Variation des Erdmagnetismus," p. 35, first footnote and p. 44.

The results here given are slight improvements upon the quantities already published.

In the "abstract" published in Science, June 21, 1895, p. 675, this was erroneously given as 50° W. instead of 30° W.

Erman and Petersen: Grundlagen der Gaussischen Theorie und die Erscheinungen des Erdmagnetismus im Jahre, 1829. Berlin, 1874. Table of computed

inclinations.

It will be observed that both poles have undoubtedly been moving westwardly during the interval from 1780 to 1885. It would appear, moreover, as though they are not moving along the equator but along a line inclined to it, from the northern to the southern side. How much reliance is to be put upon. this latter result I cannot, at present, say.

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These figures would appear to indicate that the two poles are moving westwardly and southwardly at different rates. Whether this is really the case must be the subject of a more detailed examination. It is sufficient to know, at this stage of our inquiry, the general direction and the average rate of motion.

Since the intersections of the agonic lines*-the lines marking out the places where the magnetic declination is zerowith the equator fall so nearly together with the secondary magnetic poles, it may be interesting to see how the agonic lines have been moving along the equator for the last 3 centuries. This opportunity is furnished by the table on the following page.

In the third and sixth columns are given the positions as obtained from charts giving the lines of equal magnetic declination. The fourth and seventh columns contain the computed. quantities supposing the motion to have been linear. The formula, obtained by a least square adjustment of the observations properly weighted, is for the west agonic:

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A being the longitude and t the date to which refers.

By casting the eye over the differences between the observed and computed quantities, it will be noticed that the accord is satisfactory. Plotting the observed quantities, it will readily be seen that the motion for 350 years has been nearly linear for both agonics. A very slight curvature is noticeable in the secular motion of the west agonic. In the case of the east agonic, the errors of observation (or fluctuations) are so large as to mask any slight curvature that might be present.

We have before us a most interesting result. For 3 centuries the lines of no declination have been moving apparently

* Shown on the diagrams by the broken lines.

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