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satisfied is no other than that the changes are proportional to the {rises} of
the angles of deviation which the ship's head makes with the magnetic mer-
idian; and
5^th The law by which these changes are governed in different parts of the
earth, and which is, that they are directly proportionate to the dip of the
needle at those parts ^ ^{on board a ship when her head deviates from the meridian};     thus if the change is 2° ^ ^{at a place} where the dip is 35° it will
be 4° ^{in the same case where the dip} ^ where it is 70°; provided the quantity and disproportion of
the magnetic [illegible] on the ship ^board remains the same.
        Thus far, I believe, my subject is untouched by any other ^ ^person; but in order
to prove my facts and conclusions to the satisfaction of others, I require
a regular series of observations made with this point in view, on board more than
one vessels at two or three stations widely distant.
        With respect to the magnetism situation of the magnetic poles, you will
conclude that I have much impatience to see the manuscript of M M.
Humboldt and Bist, especially as from what you say I suspect our conclusi-
ons will ^ ^nearly be the same. The points upon the surface to which the needle seems to be
most generally directed are in 74°40' N and 88°40' W in one hemisphere, and in
73°30' south and 134° east ^ ^{of Greenwich in the other;} but it appears, that America, particularly near
Cape Horn, and Madagascar, have a great effect upon the needle; the for-
mer so much so as to render it difficult to point out ^assign the situations of the ^ ^great at-
tractive points; I had besides another difficulty, and all others to this time must
have nearly had the same, which is the being obliged to make my deduc-
tions from observations which ^ ^{my own excepted} have not received the necessary corrections;
my conclusions thereon are therefor deferred until I ^ ^can make a collection
of observations in different parts of the earth, with the necessary data to
divest them of the error arising from the ship.
      Considering that the two magnetic poles of the earth must be equal in force,
and produce 90° of inclination at the point immediately above one as above
the other, I conclude that the difference between the squares of their distan-
ces must be the same at each, and ^ ^{that these squares must be} as 1 is to 2, the roots of which are 1 and
1,414214; or in parts of the semidiameter of the earth, the distances of the
poles from the points above on the surface are 0,828427 and 1,171573
the squares of which are equally the double the one of the other; they should
therefore be no more than 0,171573 of the semidiameter distant from the
center of the earth; and from what you say, I judge this is nearly M.M.
H and B's determination. These positions ^ ^{taken exactly on opposite sides of the center} give me 70 ¼ of inclination at
Paris where M. {Haüy} says it is 72° and 66° on the south coast of Aus-
tralia where I observed the same; but with four other observations nearer
the equa-