336 



motions of a magnet supposed freely suspended in the direction of 

 the magnetic force. 



I may state shortly the process by which the following results have 

 been arrived at. The corrected observations for each of the three 

 magnetometers having been discussed with reference to a particular 

 argument; such as, the month, the moon's age, the moon's position 

 in declination, the sun's hour angle, and the moon's hour angle ; the 

 motion of the (supposed) freely suspended needle at right angles to 

 the plane of the magnetic meridian, was obtained with reference to 

 the argument in multiplying the corresponding variations of declina- 

 tion by a constant factor (the cosine of the dip); the motion parallel 

 to the same plane was obtained fi-om the variations for the two com- 

 ponents by the formula already referred to ; the value of the former 

 part of the motion for any epoch being taken as the abscissa, and 

 that of the latter for the same epoch as the ordinate, the motion of 

 the north end of the needle is constructed. 



Annual Motions. — The difficulty of determining the law of an- 

 nual variation of any of the magnetic elements has been so great, 

 that it is doubtful whether that for the magnetic declination has ever 

 been obtained, though the instrument upon which its determination 

 depends is unaffected by variation of temperature. I believe that I 

 have succeeded in the determination of the laws of all the elements, 

 and from these the annual motion has been constructed. The an- 

 nual motion deduced from the observations of the three magnetome- 

 ters for the four years 1843, 1844, 1845, and 1846, is shewn in 

 figure A ; another and rather more symmetrical figure, deduced from 

 a different combination of years, is shewn in figure B, Plate VI., 

 Edin. Trans., Vol. xix.. Part 2. 



From near the vernal till the autumnal equinox the annual mo- 

 tion forms the half of an ellipse whose major axis, passing at the 

 vertex through June, makes an angle of about +11° in figure A 

 and of +16° in figure B with the projection of the magnctical me- 

 ridian. At the autumnal equinox the north end of the needle again 

 ascends till the winter solstice, after which it descends till the vernal 

 equinox. In its descent, the north end of the needle having crossed 

 its previously ascending path, it forms a loop which, when untwisted 

 and continued downwards from the equinoxes, completes the ellipse ; 

 the portion formed by the loop having almost exactly the same peri- 

 meter as that regularly formed when the sun is north of the equator ; 



