PRELIMINARY. 



direction of the terrestrial forces. In our country this direction 

 is almost north and south, and it makes a considerable angle with 

 the horizontal line, the north pole pointing downwards. 



The magnetic meridian in any place is the vertical plane passing 

 through the direction of the earth's magnetic force. 



The declination is the angle which the magnetic meridian makes 

 with the astronomical meridian ; the declination is said to be west 

 when the north pole of a free magnet turns to the west of the 

 magnetic meridian which passes through its centre ; it is east if this 

 north pole is to the east of the meridian. 



The inclination is the angle which the earth's force makes with 

 its projection on a horizontal plane. 

 Let 



D be the declination, 



I the inclination, 



T the strength of the earth's field, 



H the horizontal component = T cos I, 



Z the vertical component = T sin I. 



A magnetised needle, movable about a vertical axis, will only 

 obey the horizontal component of the earth's force, and will place 

 itself so that its axis of magnetisation is in the magnetic meridian. 

 If we move it out by an angle 8, the moment of the couple which 

 tends to bring it back, has the value 



HMsinS; 



M being the magnetic moment of the needle. It is proportional to 

 the sine of the angle of deviation. This result has been verified by 

 the very accurate experiments of Coulomb by means of his torsion 

 balance. 



If the needle is suspended freely by its centre of gravity, or is 

 movable about a horizontal axis passing through this point, and 

 perpendicular to the magnetic meridian, the direction of the mag- 

 netic axis, when the needle is in equilibrium, is the direction of the 

 earth's force itself; the angle which its magnetic axis then makes 

 with the horizontal measures the inclination. 



Let us now suppose that the horizontal axis of rotation makes 

 an angle a with the perpendicular to the magnetic meridian. We 

 may replace the horizontal component H by its two projections, the 

 one H sin a parallel to the axis of rotation, and other H cos a per- 

 pendicular to this axis. The needle only obeys the two forces Z and 



