VARIATION

VARIATION, the angle contained between the true meridian and the magnetic meridian.

After the discovery of that most useful property of the magnet, or loadstone, namely, the giving hardened iron and steel a polarity, the compass was for many years used without knowing that its direction in any wise deviated from the poles of the world: and about the middle of the 16th century, so certain were some of its inflexibly pointing to the north, that they treated with contempt the notion of the variation, which about that time began to be suspected. However, careful observations soon discovered, that in England and its neighbourhood, the needle pointed to the eastward of the true north: but the quantity of this deviation being known, mariners became as well satisfied as if the compass had none; because they imagined that the true course could be obtained by making allowance for the true variation.

From successive observations made afterwards, it was found, that the deviation of the needle from the north was not a constant quantity, but that it gradually diminished; and at last, about the year 1660, it was found at London that the needle pointed due north, and has ever since been getting to the westward of the north: so that in any one place it may be suspected the variation has a kind of libratory motion, traversing through the north to unknown limits eastward and westward. But the settling of this point must be left to time.

During the time of the said observations it was also discovered, that the variation of the needle was different in different parts of the world, it being west in some places when it was east in others; and in places where the variation was of the same name, yet the quantity of it greatly differed. It was therefore found necessary, that mariners should every day, or as often as they had opportunity, make during their voyage proper observations for an amplitude or azimuth; whereby they might be enabled to find the variation of the compass in their present place, and thence correct their courses.

Dr Halley published in the last century a theory of the variations of the compass. In this work he supposes there are four magnetic poles in the earth; two of which are fixed and two moveable, by which he explains the different variation of the compass at different times in the same place. But it is impossible to apply exact calculations to so complicated an hypothesis. M. Euler, son of the celebrated geometrician of that name, has however shown, that two magnetic poles placed on the surface of the earth will sufficiently account for the singular figure assumed by the lines which pass through all the points of equal variation in the chart of Dr Halley.

M. Euler first examines the case wherein the two magnetic poles are diametrically opposite; second, he places them in the two opposite meridians, but at un-

equal distances from the poles of the world; third, he places them in the same meridians. Finally, he considers them situated in two different meridians. These four cases may become equally important; because, if it is determined that there are only two magnetic poles, and that these poles change their situations, it may sometime hereafter be discovered that they pass through all the different positions.

Since the needle of the compass ought always to be in the plane which passes through the place of observation and the two magnetic poles, the problem is reduced to the discovery of the angle contained between this plane and the plane of the meridian. M. Euler, after having examined the different cases, finds that they also express the earth's magnetism, represented in the chart published by Mess. Mountain and Dodson in 1744, particularly throughout Europe and North America, if the following principles are established.

Between the arctic pole and the magnetic pole $14^\{\backslash circ\}\; 53\text{'}$.

Between the antarctic pole and the other magnetic pole $29^\{\backslash circ\}\; 23\text{'}$.

$53^\{\backslash circ\}\; 18\text{'}$ the angle at the north pole, formed by the meridian's passing through the two magnetic poles.

$25^\{\backslash circ\}$ the longitude of the meridian, which passes over the northern magnetic pole.

As the observations which have been collected with regard to the variation are for the most part loose and inaccurate, it is impossible to represent them all with precision; and the great variations observed in the Indian Ocean seem to require, says M. Euler, that the three first quantities should be $14$, $35$, and $65$ degrees. In the mean time, the general agreement is sufficiently satisfactory.

The high reputation of Dr Halley's magnetical chart renders it more particularly necessary to point out the errors contained therein. There is evidently too little distance between the lines of no variation, of which one crosses the equator $17^\{\backslash circ\}$ westward of London, and the other $119^\{\backslash circ\}$ to the eastward. This makes $136^\{\backslash circ\}$ only; whereas it should necessarily exceed $180$, and even $200$, inasmuch as the pole of the world is supposed further distant from the magnetic pole towards the south than in the north, as is required by the other phenomena. Again, upon the coasts discovered by Diemen, there was no variation in 1642; and Dr Halley also supposes there was none in 1700. Meanwhile, by the alteration observed at Paris, the line of no variation should be advanced $60^\{\backslash circ\}$ towards the south, which will agree better with the calculations, and prove that the distance of the two intersections was really greater than Dr Halley had established.

The table of variation of Mess. Mountain and Dodson is accompanied with several interesting particulars, which equally deserve to be inserted here.

At Barbadoes (says Captain Snow), the variation seems very nearly at a stand: for in the road I observed $5^\{\backslash circ\}$ east; and by Dr Halley's draught, in the year 1701, $5\backslash frac\{1\}\{2\}^\{\backslash circ\}$. In 1747, at Port Royal keys, Jamaica, I observed the variation $7^\{\backslash circ\}\; 20\text{'}\; E.$; and on the coast of Carthage, the same week, off the high land of Santa Martha, $7^\{\backslash circ\}\; 45\text{'}$ nearly south of Port Royal. Therefore these curves are not much altered: the curve at Jamaica is nearly at a stand, as though tied, and the south part of them with the rest dropping to the westward.

Under the equator, in longitude $40^\{\backslash circ\}$ E. of London, the highest variation during the whole 56 years appears to be $17^\{\backslash circ\}\backslash frac\{1\}\{2\}$ W. and the least $16^\{\backslash circ\}\backslash frac\{1\}\{2\}$ W.; and in latitude $15^\{\backslash circ\}$ N. longitude $60^\{\backslash circ\}$ W. from London, the variation has been constantly $5^\{\backslash circ\}$ E. But in other places the case has been widely different. For in the latitude of $10^\{\backslash circ\}$ S. longitude $60^\{\backslash circ\}$ E. from London, the variation has decreased from $17^\{\backslash circ\}$ W. to $7^\{\backslash circ\}\backslash frac\{1\}\{2\}$ W.; and in latitude $10^\{\backslash circ\}$ S. longitude $5^\{\backslash circ\}$ W. from London, from $2^\{\backslash circ\}\backslash frac\{1\}\{2\}$ W. to $12^\{\backslash circ\}\backslash frac\{1\}\{2\}$ W.; and in latitude $15^\{\backslash circ\}$ N. longitude $20^\{\backslash circ\}$, it has increased from $1^\{\backslash circ\}$ W. to $9^\{\backslash circ\}$ W.

But there is still a more extraordinary appearance in the Indian sea. For instance, under the equator:

Where the west variation, in the longitude $40^\{\backslash circ\}$ E. is the same in both the above years; and in 1700 the west variation seemed to be regularly decreasing from longitude $50^\{\backslash circ\}$ E. to the longitude $100^\{\backslash circ\}$ E.; but in 1756, we find the west variation decreasing so fast, that we have east variation in the longitude $80^\{\backslash circ\}$, $85^\{\backslash circ\}$, and $90^\{\backslash circ\}$ E. and yet in the longitude $95^\{\backslash circ\}$ and $100^\{\backslash circ\}$ E. we have west variation again.

To these remarks may be subjoined the following extracts from the Exposition du calcul astronomique, by M. de la Lande.

"At the royal observatory in Paris, a magnetical needle of four inches deviated from the N. $18^\{\backslash circ\}\; 10\text{'}$ towards the west, on the 15th of February 1759; and on the 22d of April 1760, the same needle varied $18^\{\backslash circ\}\; 20\text{'}$. It is indeed natural to conceive, that nothing can be precisely ascertained by $10\text{'}$ upon a circle whose diameter is only four inches. It is nevertheless sufficiently evident, that this variation continues to increase at Paris. In 1610 the needle declined $8^\{\backslash circ\}$ towards the east, so that the variation has changed $26^\{\backslash circ\}\; 20\text{'}$ in the space of 150 years; and this appears particularly since 1740: for the same needle, which has always been used by M. Maraldi, is more than $3^\{\backslash circ\}$ advanced towards the west, beyond what it was at that period; and this makes $9^\{\backslash circ\}$ in one year."