230 Instructions for the Scientific Expedition 



round their middle point, the magnet is maintained in a position at 

 right angles to the magnetic meridian. 



It is manifest from the nature of this suspension, that the weight 

 of the suspended body will tend to bring it into the position in which 

 the two portions of the wire are in the same plane throughout. The 

 moment of the directive force is G sin v ; — v denoting the angle 

 formed by the lines joining the bearing points above and below, or 

 the deviation from the plane of detorsion ; and G being expressed by 

 the formula 



G = t.^; 



in which w denotes the weight of the suspended body, a half the in- 

 terval of the wires, and I their length. The earth's magnetic force, on 

 the other hand, tends to bring the magnetic axis of the bar into the 

 magnetic meridian, with the force F sin u ; in which ii is the deviation 

 of the magnetic axis from the meridian, and F is the product of the 

 horizontal part of the earth's magnetic force into the moment of free 

 magnetism of the bar. The magnet being thus acted on by two 

 forces, will rest in the position in which their moments are equal. 

 When the instrument is so adjusted that u = 90°, or the magnet at 

 right angles to the magnetic meridian, 



F = G sin t; ; 



and the ratio of the forces is known, when we know the angle v. 

 But as one of these forces is constant, and the other variable, it is 

 evident that the place of the magnet will vary around its mean po- 

 sition, and that the variations of angle are connected with the varia- 

 tions of the force. This connexion is expressed by the formula 



d¥ = Fcotany .<?m; 



the angle d u being expressed in parts of radius. 



Construction. — The magnet bar is of the same dimensions as that of 

 the declination instrument. The collimator, by which its changes 

 of position are observed, is attached to the stirrup, and has a motion 

 in azimuth. The suspending wire passes round a small grooved 

 ■wheel, on the axis of which the stirrup rests by inverted Y s ; and 

 the instrument is furnished with a series of such wheels, whose dia- 

 meters increase in arithmetical progression, (the common difference 

 being about gTT^^^ °^ ^^ inch,) for the purpose of varying the interval 

 of the wires. ITie exact intervals, corresponding to each separate 

 wheel, have been determined by the artist by accurate micrometrical 

 measurements ; they are given in Table III. The same interval 

 is altered, at the upper extremity, by means of two screws (one right- 

 handed and the other left-handed) cut in the same cylinder ; the 

 wires being lodged in the intervals of the threads, and their distance 

 regulated l)y a micrometer head. The interval of the threads of this 

 screw (which is precisely the same for all the instruments) is yyths, or 

 •02597 of an inch. The micrometer head is divided into 100 parts; 

 and, as one revolution of the head corresponds to two threads of the 

 screw, a single division is equivalent to '0005194, or the ^onnth of 



